case study on coordinate geometry class 8

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• Coordinate Geometry

Co-ordinate Geometry

Coordinate Geometry is considered to be one of the most interesting concepts of mathematics. Coordinate Geometry (or the analytic geometry ) describes the link between geometry and algebra through graphs involving curves and lines. It provides geometric aspects in Algebra and enables them to solve geometric problems. It is a part of geometry where the position of points on the plane is described using an ordered pair of numbers. Here, the concepts of coordinate geometry (also known as Cartesian geometry) are explained along with its formulas and their derivations.

Introduction to Coordinate Geometry

Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc. There are certain terms in Cartesian geometry that should be properly understood. These terms include:

What is a Co-ordinate and a Co-ordinate Plane?

You must be familiar with plotting graphs on a plane, from the tables of numbers for both linear and non-linear equations. The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis ( horizontal line ) and the y-axis( vertical line ).

The four quadrants along with their respective values are represented in the graph below-

• Quadrant 1 : (+x, +y)
• Quadrant 2 : (-x, +y)
• Quadrant 3 : (-x, -y)
• Quadrant 4 : (+x, -y)

The point at which the axes intersect is known as the origin . The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates .

The figure below shows the Cartesian plane with coordinates (4,2). If the coordinates are identified, the distance between the two points and the interval’s midpoint that is connecting the points can be computed.

Coordinate Geometry Fig. 1: Cartesian Plane

Equation of a Line in Cartesian Plane

Equation of a line can be represented in many ways, few of which is given below-

(i) General Form

The general form of a line is given as Ax + By + C = 0.

(ii) Slope intercept Form 

Let x, y be the coordinate of a point through which a line passes, m be the slope of a line, and c be the y-intercept, then the equation of a line is given by:

(iii) Intercept Form of a Line

Consider a and b be the x-intercept and y-intercept respectively, of a line, then the equation of a line is represented as-

Slope of a Line: 

Consider the general form of a line Ax + By + C = 0, the slope can be found by converting this form to the slope-intercept form.

Ax + By + C = 0

⇒ By = − Ax – C

Comparing the above equation with y = mx + c,

Thus, we can directly find the slope of a line from the general equation of a line.

Coordinate Geometry Formulas and Theorems

Distance formula: to calculate distance between two points.

Let the two points be A and B, having coordinates to be (x 1 , y 1 ) and (x 2 , y 2 ), respectively.

Thus, the distance between two points is given as-

Coordinate Geometry Fig. 2: Distance Formula

Midpoint Theorem: To Find Mid-point of a Line Connecting Two Points

Consider the same points A and B, which have coordinates (x 1 , y 1 ) and (x 2 , y 2 ), respectively. Let M(x,y) be the midpoint of lying on the line connecting these two points A and B. The coordinates of point M is given as-

Angle Formula: To Find The Angle Between Two Lines

Consider two lines A and B, having their slopes m 1 and m 2, respectively.

Let “θ” be the angle between these two lines, then the angle between them can be represented as-

Special Cases:

• Case 1:  When the two lines are parallel to each other,

m 1 = m 2 = m

Substituting the value in the equation above,

• Case 2:  When the two lines are perpendicular to each other,

m 1 . m 2 = -1

Substituting the value in the original equation,

\(\begin{array}{l}\large \tan \theta = \frac{m_{1} – m_{2}}{1 + (-1)} = \frac{m_{1} – m_{2}}{0}\end{array} \) which is undefined.

Section Formula: To Find a Point Which Divides a Line into m:n Ratio

Consider a line A and B having coordinates (x 1 , y 1 ) and (x 2 , y 2 ), respectively. Let P be a point that which divides the line in the ratio m:n, then the coordinates of the coordinates of the point P is given as-

• When the ratio m:n is internal:
• When the ratio m:n is external:

Students can follow the link provided to learn more about the section formula  along its proof and solved examples.

Area of a Triangle in Cartesian Plane

The area of a triangle In coordinate geometry whose vertices are (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is

If the area of a triangle whose vertices are (x 1 , y 1 ),(x 2 , y 2 ) and (x 3 , y 3 ) is zero, then the three points are collinear.

• Important:  Click here to Download  Co-ordinate Geometry pdf

Examples Based On Coordinate Geometry Concepts

Examples 1: Find the distance between points M (4,5) and N (-3,8).

Applying the distance formula we have,

Example 2: Find the equation of a line parallel to 3x+4y = 5 and passing through points (1,1).

For a line parallel to the given line, the slope will be of the same magnitude.

Thus the equation of a line will be represented as 3x+4y=k

Substituting the given points in this new equation, we have

k = 3 × 1 + 4 × 1 = 3 + 4 = 7

Therefore the equation is 3x + 4y = 7

Coordinate Geometry Questions For Practice

• Calculate the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
• Find the area of the triangle having vertices at A, B, and C which are at points (2, 3), (–1, 0), and (2, – 4), respectively. Also, mention the type of triangle.
• A point A is equidistant from B(3, 8) and C(-10, x). Find the value for x and the distance BC.

Video Lesson on Coordinate Geometry Toughest Problems

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Frequently Asked Questions

What is abscissa and ordinates in coordinate geometry.

The abscissa and ordinate is used to represent the position of a point on a graph. The horizontal value or the X axis value is the abscissa while the vertical value i.e. the Y axis value is the ordinate. For example, in an ordered pair (2, 3), 2 is abscissa and 3 is ordinate.

What is a Cartesian Plane?

A Cartesian plane is a plane which is formed by two perpendicular lines known as the x-axis (horizontal axis) and the y-axis (vertical axis). The exact position of a point in Cartesian plane can be determined using the ordered pair (x, y).

Why do we Need Coordinate Geometry?

Coordinate geometry has various applications in real life. Some of the areas where coordinate geometry is an integral part include.

• In digital devices like computers, mobile phones, etc. to locate the position of cursor or finger.
• In aviation to determine the position and location of airplanes accurately.
• In maps and in navigation (GPS).
• To map geographical locations using latitudes and longitudes.

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• RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry
• RS Aggarwal Solutions

Introduction to Coordinate Geometry Solutions By RS Aggarwal - Free PDF Download

RS Aggarwal Class 8 Introduction to coordinate geometry is the most interesting topic in mathematics. Introduction to coordinate geometry class 8 topics is a geometry subject that shares the point positions described by a pair of numbers on the plane. It elaborates the link between algebra and geometry through graphs that involve lines and curves. It gives geometric features in algebra and allows it to solve geometry problems. The concepts of class 8 maths RS Aggarwal chapter 22 coordinate geometry are explained with formulas and derivations.

Vedantu is a platform that provides free NCERT Solution and other study materials for students. Download Class 8 Maths and Class 8 Science NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Download RS Aggarwal Solutions for Class 8 Chapter 22 in PDF

RS Aggarwal solutions class 8 maths chapter 22 is provided with step by step explanations. These are very popular among the students of class 8. Introduction to coordinate geometry solutions are convenient to complete your homework and prepare well for exams quickly. All questions and answers of RS Aggarwal class 8 maths ch 22 are given here for free and are prepared by experts with 100% accuracy. The maths’s RS Aggarwal solutions class 8 chapter 22 can be downloaded from the official website of Vedantu in a PDF format. If you have RS Aggarwal class 8 chapter 22 solution in PDF format, you can download and print to access it easily. 

RS Aggarwal Chapter 22 Class 8 Introduction to Coordinate Geometry

RS Aggarwal class 8 chapter 22 introduction to coordinate geometry is based on analytic geometry that uses coordinate points to find the distance between any two points, get the midpoint of a line, divide lines, and calculate a triangle area in the cartesian plane, and more. Certain key terms that are used in cartesian geometry include:

Coordinate Geometry: It is a study of geometry where coordinates are used to define a point. Coordinate helps to find the exact position of a point in a coordinate plane. 

Coordinate and Coordinate Plane: A cartesian plane (or a 2D plane) is divided into 4 quadrants where 2 axes are perpendicular to each other that are x-axis and y-axis where the two lines XOX' and YOY' are perpendicular to each other. 

XOX' represents the x-axis which is horizontal to the cartesian plane

YOY' represents the y axis which is vertical to the cartesian plane

Quadrants: The four quadrants which are present in the cartesian plane are as follows: 

Quadrant 1- XOY, sign (+,+)

Quadrant 2- YOX' , sign (-,+) 

Quadrant 3- X'OY' , sign (-,-)

Quadrant 4- Y'OX, sign (+,-)

Ordered Pair - Any point in the cartesian plane is represented in the form of (x,y) called an ordered pair of coordinates, where x is present in the x-coordinate called as abscissa of the point, and y is present at y-coordinate known as ordinate of the point. 

Origin - The point at which both the axis intersects with each other is known as the origin. It is the reference point with which the distance of a point on the x-axis and y-axis are measured.

Equation of A Line In The Cartesian Plane

An equation of a line can be represented in various ways such as:

The General Form of A Line: The general form of a line can be written as Ax+By+C= 0

Slope-Intercept Form: If x and y are coordinates of a point from where a line passes with am being the slope of a line which c is the y-intercept, then the equation of a line is written as: 

Intercept Form: If x and y are the x-intercept and y-intercept of a line, then the equation of a line  is written as

The Slope of a Line: Let the general form of a line is Ax+By+C= 0, the slope can be found by converting the general form of a line to slope-intercept form. 

or, By= -Ax -C

or, y = -A/B x - C/ B

Comparing this equation with the slope-intercept equation

All the Exercise questions with solutions in Chapter-22 Introduction to Coordinate Geometry Are given below:

Exercise 22.1

Exercise 22.2

The Pattern of Questions in RS Aggarwal Chapter 22, Introduction to Coordinate Geometry

Here is a look into the pattern of questions from the chapter:

There are two exercises, exercise 22A and exercise 22B discussed in RS Aggarwal Class 8 Mathematics Solutions for Chapter-22, that is, Introduction to Coordinate Geometry.

Exercise 22A contains 13 questions on introduction to coordinate geometry. These questions are based on general knowledge of the concepts of the chapter and on plotting points on a graph.

Questions where the students need to specify the abscissa and ordinate of the given coordinates are also included in RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry.

The students will also be asked to plot the points on a graph and observe the results. Through this activity, the students will see how straight lines and polygons are formed on the graph.

Exercise 22B contains three multiple-choice questions, in which the coordinates of a point are given to the students and they have to identify that in which quadrant does these points lie.

Important Questions from CBSE Class 8 Chapter 22: Introduction to Coordinate Geometry

The important concepts that students should definitely study for CBSE Class 8 Chapter 22, that is, Introduction to coordinate geometry are:

What is a Plane?

What are coordinates?

What is a coordinate plane?

What are quadrants?

What is the origin?

What are abscissa and ordinate?

What is coordinate geometry?

How to plot graphs?

How to interpret the results of a graph?

These concepts are very important for the students of Class 8 as they will form the base of the chapter that will help them in their higher classes and also during the preparation of competitive exams.

Benefits of RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry

The benefits of RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry are:

RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry will help you build a strong foundation of the concepts of coordinate geometry.

The solutions to RS Aggarwal Class 8 Chapter 22 are created by the subject experts with respect to the latest CBSE Class 8 Maths syllabus.

These solutions will help the students in exam preparation.

The solutions will build confidence in students for attempting any questions that can be asked during the examination.

The students will also be able to deal with plotting and interpreting the results of a graph.

These solutions are absolutely free for the students.

These solutions will act as a mode of revision of the concepts and formulae for the students.

Preparation Tips For Rs Aggarwal Class 8 Solutions Chapter 22

While practising coordinate geometry problems, write down the formulas in a different notebook that you can overlook daily and memorise them.

You must draw figures for every single problem for better clarification.

Solve all the textbook problems and RS Aggarwal class 8 solutions chapter 22 for maximum practice that will help you solve any question you get in the exams. 

Memorise the signs of the quadrants which will help you solve problems instantly of RS Aggarwal class 8 chapter 22

Read the question carefully before solving the problem, which will save you time. 

FAQs on RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry

1. Why do we want to co-ordinate geometry?

In real life coordinates, geometry is applied in various areas. Some important applications of coordinate geometry in real life include: 

• In navigation and maps,
• To locate the geographical locations with the help of latitude and longitudes.
• To find the location and the positions of aeroplanes correctly while in aviation.
• To look at the cursor position in digital devices such as mobile phones, laptops, computers, etc.

2. What do you mean by abscissa and ordinate in coordinate geometry? 

The abscissa and ordinates refer to the coordinates in coordinate geometry. The abscissa and the ordinates are the names given to the x-coordinate and the y-coordinate respectively. The x-coordinate (known as abscissa) is located at a given distance from the y-axis and the y-coordinate (known as ordinate) is located at a given distance from the x-axis at a point denoted by P. These coordinates are used during the construction of graphs like line graph and linear graph.

3. What do you mean by coordinate geometry? 

The branch of geometry which deals with the position of the points is defined by an ordered pair of numbers (known as coordinates). This branch of geometry is known as coordinate geometry. The abscissa and ordinates are the two major coordinates representing the x and the y-axis. Coordinates are a set of values that show the exact position of a point in the coordinate plane.

4. How can I download the RS Aggarwal Class 8 Mathematics Solutions for Chapter-22, Introduction to Coordinate Geometry?

The RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry are available at the official website of Vedantu. These RS Aggarwal solutions are available free of cost for the students by Vedantu. The students on opening the website of Vedantu will have to register on the website through their email addresses. The students can then browse through the website and download all the study material available for class 8 in the form of a PDF file.

5. How will RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry help me for my exams?

RS Aggarwal Class 8 Mathematics Solutions for Chapter-22 Introduction to Coordinate Geometry will help students prepare well for the exams. These solutions have been designed by the experts of our team, keeping the CBSE class 8 syllabus in mind. The experienced faculty at Vedantu has designed solutions in such a way that they are simple to understand and also clear all the doubts that may arise in a student’s mind pertaining to a specific topic. These solutions will also help students revise the complete syllabus and formulae in one place in a hassle-free manner.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Fundamentals of Coordinate Geometry | Concepts, Coordinate Graph, Quadrants

November 21, 2020 by Veerendra

A plane is any flat surface that can go on infinitely in both directions. Coordinate geometry or analytical geometry is the link between algebra and geometry through graphs having curves and lines. It provides geometric aspects in algebra and enables them to solve geometric problems. Get the detailed information about the coordinate graph, all four quadrants, coordinates of points, others in the following sections.

• Coordinate Geometry Definition

Coordinate geometry is one of the branches of geometry where the position of a point is defined using coordinates. Using the coordinate geometry, you can calculate the distance between two points, find coordinates of a point, plot ordered pairs, and others. The basic terms of coordinate geometry for class 8 students are listed below.

• Coordinates of a Coordinate Geometry
• Coordinate Plane

What is meant by Coordinate and Coordinate Plane?

A coordinate plane is a two-dimensional plane created by the intersection of two axes names horizontal axis (x-axis) and the vertical axis (y-axis). These lines are perpendicular to each other and meet at the point called origin or zero. the axes divide the coordinate plane into four equal sections, and each section is known as the quadrant. The number line which is having quadrants is also known as the cartesian plane.

A set of values that represents the exact position on the coordinate plane is called coordinates. Usually, it is a pair of numbers on the graph denoted as (x, y). Here, x is called the x coordinate, y is called the y coordinate.

Quadrants:  Four different quadrants and their respective signs are given below:

• Quadrant 1: In this quadrant both x and y are positive. The point is represented as (+x, +y).
• Quadrant 2: X-axis is negative and the y-axis is positive. So, the point is shown as (-x, +y).
• Quadrant 3: Here, both x and y axes are negative. The point in Q3 is represented as (-x, -y).
• Quadrant 4: In this quadrant, x is positive, and y is negative. Coordinates are (+x, -y).

How to Plot Coordinates of a Point on Graph?

Following are the simple steps to plot coordinates of a point on a graph. Have a look at them and check out how to plot a graph, represent ordered points, and identify signs of axes of a point.

• First of all, take a point which is having both x coordinate ad y coordinate.
• And know the signs of each value in the given point.
• Using those signs, identify under which quadrant the point falls.
• From the respective axes, take those numbers and put a dot on the graph.

Linear Equation

The general form of a line in the coordinate geometry is Ax + By + C = 0

Where A is the coefficient of x

B is the coefficient of y

And C is the constant value.

Intercept form of a line is y = mx + c. Where (x, y) is a point on the line and m is the slope.

Graph of Area vs. Side of a Square

To plot a graph of the square area and square side, you need to have the square area for each side length. Measure the square side length each time, find the area by performing the square of side length. Note down those values and take side length on the x-axis, area on the y-axis. As the square side is always positive, the points will automatically come in the first quadrant. Mark points such as side length as x-coordinate and area as y-coordinate for each point in the graph. Join those points to make a graph of area vs square side length.

Graph of Distance vs. Time

Drawing the graph for area vs side of a square and distance vs time is the same. Here, we are checking the distance traveled by an object in a certain amount of time, what happens when a change happens in either time or distance. Make sure that, the unit of both time and distance must be the same, if not convert them into the same unit. Take distance on the y-axis and time on the x-axis, so the x coordinate will the time, and the y coordinate will be the distance. Mark those points in the first quadrant and join them to draw a graph of distance vs time.

Example Questions

Plot that the points A (0, 0), B (1, 1), C (2, 2), D (3, 3) and show that these points form a line?

Given Points are A (0, 0), B (1, 1), C (2, 2), D (3, 3)

Point A (0, 0) is the origin.

From the graph, we can say that the points form a straight line and that line passes through the origin.

Plot each of the following points on a graph?

a. (5, 2) b. (8, 0) c. (-5, -2) d. (9, -1)

Given points are (5, 2), (8, 0), (-5, -2), (9, -1)

Coordinates of the point (5, 2) both abscissa and ordinate are positive so the point lies in the first quadrant. On the x-axis, take 5 units to the right of the y-axis and then on the y-axis, take 2 units above the x-axis. Therefore, we get the point (5, 2).

Coordinates of the point (8, 0) both abscissa and ordinate are positive so the point lies in the first quadrant. On the x-axis take 8 units and take 0 units on the y-axis to get the point (8, 0).

For the point (-5, -2), both abscissa and ordinate are negative so the point lies in the third quadrant. Take -5 units on the x-axis and take -2 units on the y-axis to obtain the point (-5, -2).

The point (9, -1) lies in the fourth quadrant because x-coordinate is positive and y-coordinate is negative. To plot this point, take 9 units on the x-axis and take -1 units on the y-axis.

Draw the graph of the linear equation y = x + 1?

Given linear equation is y = x + 1

The given equation is in the form of y = mx + c

slope m = 1, and constant c = 1

By using the trial and error method, find the value of y for each value of x.

If x = 0, y = 0 + 1, then y = 1

If x = 1, then y = 1 + 1 = 2

If x = 2, then y = 2 + 1 = 3

Plot the graph for the points mentioned in the above table.

Mark the points (0, 1), (1, 2), (2, 3) on the graph.

Join those points to get a line equation.

FAQs on Coordinate Geometry

1. Why do we need coordinate geometry?

Coordinate geometry has various applications in real life. Some places where we use coordinate geometry is in integration, in digital devices such as mobiles, computes, in aviation to determine the position and location of airplane accurately in GPS, and to map the geographical locations using longitudes and latitudes.

2. Who is the father of Coordinate Geometry?

The father of coordinate geometry is Rene Descartes.

3. What is the name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane?

The name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane is determined by the x-axis and y-axis respectively.

4. What is Abscissa and Ordinates in Coordinate Geometry?

Abscissa and Ordinates are used to identify the position of a point on the graph. The horizontal value or x-axis is called the abscissa and the vertical line or the y-axis is called the ordinate. For example, in an ordered pair (1, 8), 2 is abscissa and 8 is ordinate.

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• Coordinate Geometry

Do you remember what a plane is? A plane is any flat surface which can go on infinitely in both of the directions. Now, if there is a point on a plane , you can easily locate that point with the help of coordinate geometry. Using the two numbers of the coordinate geometry, a location of any point on the plane can be found. Let us know more!

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates .

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What are Coordinates?

Now, to help you understand the coordinates, take a look at the figure below.

Now, consider the grid on the right. The columns of the grid are labeled as A, B, C, D, E, F, etc. On the other hand, the rows are numbered as 1, 2, 3, 4, 5, 6, and so on. You can see that the letter X is located in the box D3 i.e. column D and row 3.  Here, D and 3 are the coordinates of this box.

The box has two parts – one is the row and the other is the column. You need to understand that there are several boxes in every row and several boxes in every column. So, when you have both of them, you can find one single box that is the point where the rows and the columns intersect each other.

Download Coordinate Geometry Cheat Sheet Below

Browse more Topics Under Coordinate Geometry

• Areas of Triangles and Quadrilaterals
• Distance Formula
• Section Formula

The Coordinate Plane

In the coordinate geometry, all the points are located on the coordinate plane. Take a look at the figure below.

The figure above has two scales – One is the X-axis which is running across the plane and the other one is the y-axis which is at the right angles to the X-axis. This is similar to the concept of the rows and columns that we discussed in the first part above.

Understanding the Concept of Coordinates

• The point of intersection of the x and the y-axis is known as the origin . At this point, both x and y are 0.
• The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
• Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative.
• When you have to locate a point on the plane, it is determined by a set of two numbers . So, first, you have to write about its location on the x-axis followed by its location on the y-axis. Together, the two will determine a single and unique position on the plane.

So, in the figure above, the point A has a value 20 on the x-axis and value 15 on the y-axis. These are also the coordinates of the point A. Often these points are also regarded as the “rectangular coordinates”. Please note: The order of the points on the plane is crucial. You have to write the x coordinate ahead of the y coordinate.

Things That Have Been Made Possible By Coordinate Geometry

If you know the coordinates of a group of points, you can do the following:

• Determine the distance between these points.
• Find the equation , midpoint, and slope of the line segment.
• Determine if the given lines are perpendicular or parallel.
• Find the perimeter and the area of the polygon formed by the points on the plane.
• Transform the shape by reflecting, moving and rotating it.
• Define the equations of ellipses , curves , and circles .

Question For You

Question 1: What is the name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane?

Answer : The name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane are determined by x-axis and y-axis respectively.

Question 2: Who is the father of coordinate geometry?

Answer:   The father of coordinate geometry was René Descartes. He was referred to as the father of analytical geometry due to his contributions to the field. As his Latin name was Renatius Cartesius, thus we learn that the terms ‘Cartesian plane’ and ‘Cartesian coordinate system’ were a derivative of this man’s name.

Question 3: What do we need to coordinate geometry for?

Answer: Coordinate geometry is needed to offer a connection between algebra and geometry with the use of graphs of lines and curves. It is an essential branch of math and usually assists us in locating points in a plane. Moreover, it also has many uses in fields of trigonometry, calculus, dimensional geometry and more.

Question 4: What is Section Formula?

Answer: Section formula helps us knowing the coordinates of the points that are dividing a given line segment into two parts. This allows the lengths to be in the ratio m: n m: n m: n. Thus, the midpoint of a line segment is the point which divides a line segment into two equal halves.

Question 5: What is the definition of coordinate geometry in math?

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Coordinate Geometry

Every place on this planet has coordinates that help us to locate it easily on the world map. The coordinate system of our earth is made up of imaginary lines called latitudes and longitudes. The zero degrees 'Greenwich Longitude' and the zero degrees 'Equator Latitude' are the starting lines of this coordinate system.  Similarly locating the point in a plane or a piece of paper, we have the coordinate axes with the horizontal x-axis and the vertical y-axis.

Coordinate geometry is the study of geometric figures by plotting them in the coordinate axes. Figures such as straight lines, curves, circles, ellipse, hyperbola, polygons, can be easily drawn and presented to scale in the coordinate axes. Further coordinate geometry helps to work algebraically and study the properties of geometric figures with the help of the coordinate system.

What Is Coordinate Geometry?

Coordinate geometry is an important branch of math, which helps in presenting the geometric figures in a two-dimensional plane and to learn the properties of these figures. Here we shall try to know about the coordinate plane and the coordinates of a point, to gain an initial understanding of Coordinate geometry. 

Coordinate Plane

A cartesian plane divides the plane space into two dimensions and is useful to easily locate the points. It is also referred to as the coordinate plane . The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0). Further, any point in the coordinate plane is referred to by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis.

The properties of the point represented in the four quadrants of the coordinate plane are: 

• The origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).
• The x-axis to the right of the origin O is the positive x-axis and to the left of the origin, O is the negative x-axis. Also, the y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis.
• The point represented in the first quadrant (x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis. 
• The point represented in the second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive y-axis.
• The point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis.
• The point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.

Coordinates of a Point

A coordinate is an address, which helps to locate a point in space. For a two-dimensional space, the coordinates of a point are (x, y). Here let us take note of these two important terms.

• Abscissa:  It is the x value in the point (x, y), and is the distance of this point along the x-axis, from the origin
• Ordinate:   It is the y value in the point (x, y)., and is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.

The coordinates of a point are useful to perform numerous operations of finding distance, midpoint, the slope of a line, equation of a line.

Topics Covered in Coordinate Geometry

The topics covered in coordinate geometry helps in the initial understanding of the concepts and formulas required for coordinate geometry.  The topics covered in coordinate geometry are as follows.

• About the Coordinate plane and the terms related to the coordinate plane.
• Know about the coordinates of a point and how the point is written in different quadrants.
• Formula to find the distance between two points in the coordinate plane.
• The formula to find the slope of a line joining two points.
• Mid-point Formula to find the midpoint of the line joining two points.
• Section Formula to find the points dividing the join of two points in a ratio.
• The centroid of a triangle with the given three points in the coordinate plane.
• Area of a triangle having three vertices in the coordinate geometry plane
• Equation of a line and the different forms of equations of a line

Coordinate Geometry Formulas

The formulas of coordinate geometry help in conveniently proving the various properties of lines and figures represented in the coordinate axes. The formulas of coordinate geometry are the distance formula, slope formula, midpoint formula, section formula, and the equation of a line. Let us know more about each of the formulas in the below paragraphs.

Coordinate Geometry Distance Formula

The distance between two points \((x_1, y_1)\) and \(x_2, y_2) \) is equal to the square root of the sum of the squares of the difference of the x coordinates and the y-coordinates of the two given points. The formula for the distance between two points is as follows.

D = \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Slope Formula

The slope of a line is the inclination of the line. The slope can be calculated from the angle made by the line with the positive x-axis, or by taking any two points on the line. The slope of a line inclined at an angle θ with the positive x-axis is m = Tanθ.  The slope of a line joining the two points \((x_1, y_1)\) and \(x_2, y_2) \) is equal to m = \( \frac {(y_2 - y_1)}{(x_2 - x_1)} \).

m = \((y_2 - y_1)\)/\((x_2 - x_1)\)

Mid-Point Formula

The formula to find the midpoint of the line joining the points  \((x_1, y_1)\) and \(x_2, y_2) \) is a new point, whose abscissa is the average of the x values of the two given points, and the ordinate is the average of the y values of the two given points. The midpoint lies on the line joining the two points and is located exactly between the two points.

\((x, y) =\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)\)

Section Formula in Coordinate Geometry

The section formula is useful to find the coordinates of a point that divides the line segment joining the points \((x_1, y_1)\) and \((x_2, y_2)\) in the ratio \(m : n\). The point dividing the given two points lies on the line joining the two points and is available either between the two points or outside the line segment between the points.

\((x, y) = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right) \)

The centroid of a Triangle

The centroid of a triangle is the point of intersection of medians of a triangle. (Median is a line joining the vertex of a triangle to the mid-point of the opposite side.). The centroid of a triangle having its vertices A\((x_1, y_1)\), B\((x_2, y_2)\), and C\((x_3, y_3)\) is obtained from the following formula.

\((x, y) = (\dfrac{x_1+ x_2 + x_3}{3}, \dfrac{y_1 + y_2 + y_3}{3})\)

Area of a Triangle Coordinate Geometry Formula

The area of a triangle having the vertices A\((x_1, y_1)\), B\((x_2, y_2)\), and C\((x_3, y_3)\) is obtained from the following formula. This formula to find the area of a triangle can be used for all types of triangles.

Area of a Triangle = \(\dfrac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

How to Find Equation of a Line in Coordinate Geometry?

This equation of a line represents all the points on the line, with the help of a simple linear equation. The standard form of the equation of a line is ax + by + c= 0. There are different methods to find the equation of a line. Another important form of the equation of a line is the slope-intercept form of the equation of a line (y = mx + c).  Here m is the slope of the line and c is the y-intercept of the line. Further, the other forms of equations of a line such as point-slope form, two-point form, intercept form, and the normal form, are presented in the equation of a line webpage of cuemath.

Related Topics to Coordinate Geometry

• Cartesian Coordinates
• Distance Formula
• Distance Between Two Points
• Midpoint Formula
• Equation of a Line
• Three Dimensional Distance Formula
• Distance of a Point From a Line
• Slope-Intercept Form of a Line
• Point Slope Form
• Euclidean Distance Formula

Tips And Tricks on Coordinate Geometry

• The slope of the x-axis is 0 and the slope of the y-axis is \(\infty\).
• The equation of x-axis is y = 0 and the equation of y-axis is x = 0
• A point on the \(x\)-axis is of the form (a, 0), and a point on the y-axis is of the form (0, b)
• Point Slope Form of equation of a line is  \((y - y_1) = m(x - x_1) \).
• Two Point Form of equation of a line is \(y - y_1 = \left(\dfrac{y_2 - y_1}{x_2 - x_1}\right).(x - x_1) \)
• The slope Intercept Form of the equation of a line is y = mx + c 
• For two parallel lines in the coordinate plane, their slopes are equal.
• And for two perpendicular lines in the coordinate plane, the product of the slopes is equal to -1.

Solved Examples on Coordinate Geometry

Example 1: Ron is given the coordinates of one end of the diameter of a circle as (5, 6) and the center of the circle as (-2, 1).  Using the formulas of coordinate geometry how can we help Ron to find the other end of the diameter of the circle?

Let \(AB\) be the diameter of the circle with the coordinates of points \(A \), and \(B\) as follows.  

\( A = (x_1, y_1) \), \(B = (x_2, y_2)  = (5, 6)\)

The coordinates of the center \(O = (x, y) = (-2, 1)\) 

The coordinate geometry formula for midpoint of the line is:

\[ (x, y) = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right) \]

Applying this we have the following calculations.

\[\begin{align}   (-2, 1) &=\left (\frac{x_1 + 5}{2}, \frac{y_1 + 6}{2}\right) \end{align} \]

Here we shall segregate the coordinates and the \(x\) value is:

\[\begin{align}   \dfrac{x_1 + 5}{2} &= -2 \\x_1 + 5 &= -2 \times 2\\x_1 + 5 &=-4 \\ x_1 &=-4 -5 \\x_1 &= -9  \end{align} \]

And the \(y\) value is:

\[\begin{align}   \dfrac{y_1 + 6}{2} &= 1 \\y_1 + 6&= 1 \times 2\\y_1 + 6 &=2 \\ y_1 &=2 - 6 \\y_1 &= -4  \end{align} \]

Therefore the point \(A = (x_1, y_1) = (-9, -4)\)

Answer: Therefore the other end of the diameter is (-9, -4).

Example 2: Find the equation of a line passing through (-2, 3) and having a slope of -1.

The point on the line is \((x_1, y_1) = (-2, 3)\) , and the slope is \(m = -1\).

Using the coordinate geometry point and slope form of the equation of the line, we have:

\[\begin{align}(y - y_1) &= m(x - x_1) \\ (y - 3) &=(-1)(x -(-2)) \\ y - 3 &= -(x + 2) \\ y - 3 &= -x -2 \\ x + y  &= 3 - 2 \\ x + y  &= 1\end{align} \]

Answer: Therefore the equation of the line is x + y = 1.

Example 3: Find the equation of a line having a slope of -2 and \(y\)-intercept of 1.  

The given information is \(m = -2\) and \(y\)-intercept is \( c = 1\) 

From coordinate geometry we can use the slope intercept form of equation of a line.

\[\begin{align} y &= mx + c \\ y &= (-2)x + 1 \\ y &= -2x + 1  \\ 2x + y &= 1\end{align} \]

Answer: Therefore the equation of the line is 2x + y = 1.

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Practice Questions on Coordinate Geometry 

Faqs on coordinate geometry.

Coordinate Geometry is helpful to define the points in space. For this, the primary axis of the x-axis and y-axis is defined and then the points are measured and marked with reference to these points. Further, the various geometric figures such a line, curve, circle, ellipse, hyperbola, can be plotted in the coordinate axes and we can study the various properties of these geometric figures.

What Is Distance Formula in Coordinate Geometry?

The distance formula is useful to find the distance between two points in a coordinate plane. For points \((x_1, y_1)\) and \((x_2, y_2)\), the formula to find the distance is D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

What is Slope in Coordinate Geometry?

The slope of a line can be found in two ways in coordinate geometry. For the given angle of inclination θ of the line with the positive x-axis, the slope of the line is m = Tanθ. For the given two points  \((x_1, y_1)\) and \((x_2, y_2)\), on the line, the slope of the line is equal to m = \(\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\).

What Are Collinear Points in Coordinate Geometry?

The collinear points in coordinate geometry refer to a set of points that lie on the same line. The condition for three points to be collinear is that the largest distance between two points is equal to the sum of the distances between the other two sets of points. Also, the collinear points can be found using the slope formula. The slope of the line joining two points should be equal to the slope of the line joining the other two points.

Where Is Coordinate Geometry Used in Maths?

The concepts of coordinate geometry have wide applications in math. The topis of maths such as vectors, three-dimensional geometry, equations, calculus, complex numbers, functions have numerous applications of coordinate geometry. All of these topics require the data to be graphically presented in a two/three-dimensional coordinate plane.

What is Section Formula in Coordinate Geometry?

The section formula is useful to find the coordinates of a point which divides the line segment joining the points \((x_1, y_1)\) and \((x_2, y_2)\) in the ratio \(m : n\). The point dividing the line segment lies on the line joining the two points, and is either present between the two points or is beyond the two points. The formula to find the required point is: \((x, y) = \left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right) \)

How to Find the Area of Triangle in Coordinate Geometry?

The area of a triangle joining the three points  \((x_1, y_1)\),  \((x_2, y_2)\), and  \((x_3, y_3)\) in the coordinate system is \( \frac {1}{2}.|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\). The modulus symbol is used in the formula, since the area is always a positive value. 

How Is Coordinate Geometry Used in Real Life?

There are numerous applications of coordinate geometry in our real life. The maps we use to locate places: google maps, physical maps, are all based on the coordinate system. Further, it is helpful in large-scale land projects to draw the land maps to scale. The naval engineers use coordinate systems, to locate any point in the seas.

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Case Study Questions for Class 10 Maths Chapter 7 Coordinate Geometry

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

The top of a table is shown in the figure given below:

(i) The coordinates of the points H and G are respectively (a) (1, 5), (5, 1) (b) (0, 5), (5, 0) (c) (1, 5), (5, 0) (d) (5, 1), (1, 5)

(ii) The distance between the points A and B is (a) 4 units (b) 4 2 units (c) 16 units (d) 32 units

(iii) The coordinates of the mid point of line segment joining points M and Q are (a) (9, 3) (b) (5, 11) (c) (14, 14) (d) (7, 7)

(iv) Which among the following have same ordinate? (a) H and A (b) T and O (c) R and M (d) N and R

(v) If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is (a) H (b) F (c) Q (d) R

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Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)

Cbse's question bank on case study for class 10 maths chapter 7 is available here. practice this new type of questions to score good marks in your board exam..

Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry

CASE STUDY 1:

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.

1. Find the position of green flag

b) (2,0.25)

d) (0, -25)

Answer:  a) (2,25)

2. Find the position of red flag

Answer: c) (8,20)

3. What is the distance between both the flags?

a) √41

b) √11

c) √61

d) √51

Answer: c) √61

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

d) (2.5,20)

Answer: a) (5, 22.5)

5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

Answer: a) (3.5,24)

CASE STUDY 2:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

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CBSE Class 10 Maths Best Study Material for 2021-2022

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Solved MCQ: Coordinate Geometry - Case Based Type Questions | Mathematics (Maths) Class 9 PDF Download

Five friends playing a game in which they are standing at different positions, P, S, T, R and

Rohan is watching them playing. Few questions came to Rohan's mind while watching the game. Give answer to his questions by looking at the figure. Q1. Name the point whose y-co-ordinate is zero : (a)  P (b)  Q (c)  R (d)  S Ans:  b Sol:  As point Q lies on x-axis. Therefore, its y-coordinate is zero.

Q2. Name the point lying in the third quadrant. (a)  R (b)  P (c)  Q (d)  T Ans:  a Sol:  In third quadrant, both x-co-ordinate and y-coordinate are negative.

Q3. What are the coordinates of P? (a)  (– 1, 1) (b)  (1, – 1) (c)  (1, 1) (d)  (– 1, – 1) Ans:  c Sol:  The Coordinate of P is (1, 1)

Q4. Name the polygon formed on joining all these points . (a)  Quadrilateral (b)  Hexagon (c)  Pentagon (d)  Triangle Ans:  c Sol:   Pentagon (5 sided polygon).

Sohan draws a gate of a temple on the graph paper. He has following points : (– 1, 0), (1, 0), (1, 1), (– 1, 1) and (0, 2)  

Q1. In which quadrant (– 1, 1) lies ? (a)  1 st quadrant (b)  2 nd quadrant (c)  3 rd quadrant (d)  4 th quadrant Ans:  b Sol:  In 2 nd quadrant, x-co-ordinate is negative and y-coordinate is positive.

Q2. Write the abscissa of the point (0, 2). (a)  0 (b)  2 (c)  – 2 (d)  1 Ans:  a Sol:  x-co-ordinate of a point also called abscissa.

Q3. Name the closed figure obtained. (a)  Triangle (b)  Quadrilateral (c)  Pentagon (d)  Hexagon Ans:  c Sol:  A pentagon has five sides.

Q4. Write the ordinate of the point (1, 0). (a)  1 (b)  0 (c)  2 (d)  – 1 Ans:  b Sol:  y-co-ordinate of a point also called ordinate.

Q5. Which point from the following lies on Y-axis ? (a)  (1, 1) (b)  (1, 0) (c)  (0, 2) (d)  (– 1, 1) Ans:  c Sol:  On Y-axis, x-co-ordinate is zero.

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

By QB365 on 08 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Coordinate geometry case study questions with answer key.

9th Standard CBSE

Final Semester - June 2015

Mathematics

(b) What are the coordinates of C and D respectively?

(c) What is the distance between B and D?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?  

(b) What are the coordinates of A and B respectively?

(c) The coordinates of point O in the sketch -2 is

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is 

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

*****************************************

Coordinate geometry case study questions with answer key answer keys.

(a) (iii) A(3, 5); B(7, 9) (b) (i) C(11, 5); D(7, 1) (c) (iii) 8 units (d) (iii) 8 units (e) (i) (7, 5)

(i) (b) (2, 3) (ii) (a) (2, -1) (iii) (a) 4 (iv) (d) (6, 2) (v) (b) II

(a) (ii) A(13, 10); B(19, 10) (b) (iv) A(19, 6); B(13, 6) (c) (ii) (16, 8) (d) (i) (0, 8) (e)  (ii) (16, 0)

(a) (iv) C(10, 6) (b) (iii) R(5, 6) (c) (ii)   \(\sqrt{34}\)  units PS 2 = AS 2 + AP 2 = 5 2 + 3 2 = 25 + 9 = 34 ⇒ PS =  \(\sqrt{34}\) (d) (iv) Rhombus (e) (i) 30 sq. units Area of rhombus =  \(1 / 2\)  x product of diagonals =  \(1 / 2\)  x 6 x 10  = 30 sq. units

(i) (d) (-4, 3)  (ii) (b) (-3, -2) (iii) (b) (8, 4.5) (iv) (d) IV (v) (b) 10 units

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Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

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Case study Questions in Class 9 Mathematics Chapter 3  are very important to solve for your exam. Class 9 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 3 Coordinate Geometry

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In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 3 Coordinate Geometry

Case Study/Passage-Based Questions

Answer: (d) 2 units

(ii) How far is the library from Shaguns house?

Answer: (b) 2 units

(iii) How far is the library from Alia’s house?

Answer: (d) None of these

(iv) Which of the following is true?

Answer: (b) ABC forms an isosceles triangle

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of house from grocery store to that from electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to the food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 3 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE Class 10 Maths: Case Study Questions of Chapter 7 Coordinate Geometry PDF Download

Case study Questions in the Class 10 Mathematics Chapter 7  are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 7  Coordinate Geometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Based Questions (MCQ)

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Question 1 - Case Based Questions (MCQ) - Chapter 7 Class 10 Coordinate Geometry

Last updated at April 16, 2024 by Teachoo

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag

This question is inspired from  Ex 7.2, 3 - Chapter 7 Class 10 - Coordinate Geometry

Find the position of green flag (a) (2, 25) (b) (2, 0.25) (c) (25, 2) (d) (0, –25)

Find the position of red flag (a) (8, 0) (b) (20, 8) (c) (8, 20) (d) (8, 0.2)

What is the distance between both the flags? (a) √41 (b) √11 (c) √61  (d) √51

If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? (a) (5, 22.5) (b) (10, 22) (c) (2, 8.5) (d) (2.5, 20)

If Joy has to post a flag at one-fourth distance from green flag, in the line segment joining the green and red flags, then where should he post his flag? (a) (3.5, 24) (b) (0.5, 12.5) (c) (2.25, 8.5) (d) (25, 20)

Question In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag Given that there are 100 flowers between A & D at 1m distance each Niharika runs 1/4th of the distance AD on 2nd line So, Niharika’s x−cordinate = 2 Niharika’ y – cordinate = 1/4 × 100 = 25 ∴ Coordinates of Niharika = G (2, 25) Also, Preet runs 1/5th of the distance AD on 2nd line So, Preet’s x−ordinate = 8 Preet’s y – ordinate = 1/5 × 100 = 20 ∴ Coordinates of Preet = R (8, 20) Putting values in formula NP = √(( 8 −2)2+(20 −25)2) = √((6)2+(−5)2) = √((6)2+(5)2) = √(36+25) = √61 Hence, The distance between both flags = √𝟔𝟏 metres Question 1 Find the position of green flag (a) (2, 25) (b) (2, 0.25) (c) (25, 2) (d) (0, –25) Position of green flag = Point G = (2, 25) So, the correct answer is (a) Question 2 Find the position of red flag (a) (8, 0) (b) (20, 8) (c) (8, 20) (d) (8, 0.2) Position of green flag = Point R = (8, 20) So, the correct answer is (c) Question 3 What is the distance between both the flags? (a) √41 (b) √11 (c) √61 (d) √51 Distance between both flags = RG = √(( 𝟖 −𝟐)𝟐+(𝟐𝟎 −𝟐𝟓)𝟐) = √((6)2+(−5)2) = √((6)2+(5)2) = √(36+25) = √𝟔𝟏 m So, the correct answer is (c) Question 4 If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? (a) (5, 22.5) (b) (10, 22) (c) (2, 8.5) (d) (2.5, 20) Since Rashmi had to post a blue flag exactly halfway between the line segment joining the two flags It will be the mid-point of RG Thus, our diagram looks like Here, x = (𝑥1 + 𝑥2)/2 and y = (𝑦1 + 𝑦2)/2 Substituting the value in the formula x = (𝒙𝟏 + 𝒙𝟐)/𝟐 x = (2 + 8)/2 x = 10/2 x = 5 y = (𝒚𝟏 + 𝒚𝟐)/𝟐 y = (25 + 20)/2 y = 45/2 y = 22.5 ∴ Rashmi (x, y) = (5, 22.5) So, the correct answer is (a) Question 5 If Joy has to post a flag at one-fourth distance from green flag, in the line segment joining the green and red flags, then where should he post his flag? (a) (3.5, 24) (b) (0.5, 12.5) (c) (2.25, 8.5) (d) (25, 20) Now, Joy had to post a flag at one-fourth distance from green flag, in the line segment joining the green and red flags Thus, Distance between Green Flag & Joy = 1/4 × Distance between Green and Red Flag GJ = 𝟏/𝟒 × GR GJ = 1/4 × (GJ + JR) GJ = 1/4 × GJ + 1/4 × JR GJ − 1/4 × GJ = 1/4 × JR 3/4 × GJ = 1/4 × JR 𝑮𝑱/𝑱𝑹=𝟏/𝟑 Thus, Joy divides GR in the ratio 1:3 Finding x x = (𝑚1 𝑥2 + 𝑚2 𝑥1)/(𝑚1 + 𝑚2) Where, m1 = 1, m2 = 3 x1 = 2, x2 = 8 Putting values x = (1 × 8 + 3 × 2)/(1 + 3) x = (8. + 6)/4 x = 14/4 x = 3.5 Finding y y = (𝑚1 𝑦2 + 𝑚2 𝑦1)/(𝑚1 + 𝑚2) Where, m1 = 1, m2 = 3 y1 = 25, y2 = 20 Putting values y = (1 × 20 + 3 × 25)/(1 + 3) y = (20 + 75 )/4 y = (95 )/4 y = 23.75 Thus, Required Point = (3.5, 23.75)

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Case Study on Coordinate Geometry Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Coordinate Geometry Class 10 Maths can use this page to download the PDF file. 

The case study questions on Coordinate Geometry are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Coordinate Geometry case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Coordinate Geometry Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Coordinate Geometry, therefore, they prepared a set of solutions along with the case study questions on Coordinate Geometry.

The case study on Coordinate Geometry Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Coordinate Geometry case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Coordinate Geometry Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Coordinate Geometry case study questions on Class 10 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Coordinate Geometry Case study questions as it will help better prepare for the Class 10 board exam preparation.
• Develop Problem-Solving Skills: Class 10 Maths Coordinate Geometry case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
• Understand Real-Life Applications: Several Coordinate Geometry Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Coordinate Geometry as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Coordinate Geometry?

Students can choose their own way to answer Case Study on Coordinate Geometry Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Coordinate Geometry Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Coordinate Geometry questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Coordinate Geometry Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Coordinate Geometry?

 A few essential things to know to solve Case Study Questions on Class 10 Coordinate Geometry are -

• Basic Formulas of Coordinate Geometry: One of the most important things to know to solve Case Study Questions on Class 10 Coordinate Geometry is to learn about the basic formulas or revise them before solving the case-based questions on Coordinate Geometry.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Coordinate Geometry case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Coordinate Geometry Class 10 Maths?

Use Selfstudys.com to find Case Study on Coordinate Geometry Class 10 Maths. For ease, here is a step-wise procedure to download the Coordinate Geometry Case Study for Class 10 Maths in PDF for free of cost.

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• Search Maths and then navigate to the Coordinate Geometry Class 10 Maths Case Study

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