NCERT Solutions for Class 9 Maths Chapter 3 - Coordinate Geometry

Class 9 Maths Chapter 3, "Coordinate Geometry", includes three exercises that each focus on a specific set of questions. Here is a detailed explanation of each exercise:

• Exercise 3.1: This exercise introduces the fundamental concepts of coordinate geometry and aims to familiarise students with terms like the Cartesian plane, coordinates of points, quadrants, distance formula, and section formula. Additionally, students learn how to find the midpoint of a line segment and the area of a triangle.

• Exercise 3.2: This exercise explores different forms of equations of a straight line. Students are expected to find the equation of a straight line that passes through two given points. They will also learn how to find the slope and intercept of a line, and how to write the equation of a line in different forms such as slope-intercept form, point-slope form, and general form.

• Exercise 3.3: This exercise delves into the geometrical representation of linear equations. Students are tasked with plotting the graph of a linear equation on the Cartesian plane and identifying the intercepts, slope, and other characteristics of the graph. They will also learn how to find the equation of a line given its graph and how to write the equation of parallel and perpendicular lines.

Access NCERT Solutions for Maths Class - 9 Chapter 3 - Coordinate Geometry

Exercise 3.1

1. How will you describe the position of a table lamp on your study table to another person?

Ans: Consider the figure of a study stable given below, on which a study lamp is placed.

Consider the table as the rectangular plane and the lamp as a point. This table has a short edge and a long edge.

We can see that the distance of the lamp from the shorter edge is $15\ \text{cm}$ and from the longer edge, its $25\ \text{cm}$.

Therefore, depending on the order of the axes, we can conclude that the position of the lamp on the table can be described as $\left( 15,25 \right)$ or $\left( 25,15 \right)$.

2. (Street Plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are \[200\text{ }m\] apart. There are $5$ streets in each direction. Using \[1\text{ }cm\text{ }=\text{ }200\text{ }m\] , draw a model of the city in your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross- street is made by two streets, one running in the North–South direction and another in the East–West direction. Each cross street is referred to in the following manner: If the \[2nd\]  street running in the North–South direction and 5th in the East–West direction meet at some crossing, then we will call this cross-street \[\left( 2,\text{ }5 \right)\]. Using this convention, find:

i) How many cross - streets can be referred to as \[\left( 4,\text{ }3 \right)\] .

Ans: Draw two perpendicular lines depicting the two main roads of the city that cross each other at the center.

Mark it as \[NS\] and \[EW\] .

Consider the scale as \[1\text{ }cm\text{ }=\text{ }200\text{ }m\] .

Get the Figure given below by drawing five streets that are parallel to both the main roads,

From the Figure, we can see that there is only one cross street, which can be referred as \[\left( 4,\text{ }3 \right)\].

ii) How many cross - streets can be referred to as \[\left( 3,\text{ }4 \right)\] .

Ans: From the Figure, we can see that there is only one cross street, which can be referred to as \[\left( 3,\text{ }4 \right)\] .

Exercise 3.2

1. Write the answer of each of the following questions:

i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans:  X-axis is referred to as the horizontal line that is drawn to determine the position of any point in the Cartesian plane. Y-axis is the vertical line that is drawn to determine the position of any point in the Cartesian plane.

ii) What is the name of each part of the plane formed by these two lines?

Ans: Quadrant is the name of each part of the plane that is formed by x-axis and y-axis.

iii) Write the name of the point where these two lines intersect.

Ans: Origin $O$ is the point of intersection of \[x\] - axis and the $y$ - axis.

2. See the Figure, and write the following:

i) The coordinates of \[B\].

Ans: Coordinates of point \[B\] is the distance of \[B\] from $x$ - axis and \[y\] - axis.

Therefore, the coordinates of point \[B\] are \[(-5,2)\].

ii) The coordinates of \[C\].

Ans: Coordinates of point \[C\] is the distance of point \[C\] from \[x\] - axis and \[y\] -axis.

Therefore, the coordinates of point \[C\] are \[(5,-5)\].

iii) The point identified by the coordinates \[(-3,-5)\].

Ans: The point that represents the coordinates \[(-3,-5)\]  is \[E\].

iv) The point identified by the coordinates \[(2,-4)\].

Ans: The point that represents the coordinates $(2,-4)$ is \[G\].

v) The abscissa of the point \[D\].

Ans: The abscissa of point \[D\] is the distance of point \[D\] from the $y$ - axis. Therefore, the abscissa of point \[D\] is $6$.

vi) The ordinate of the point \[H\].

Ans: The ordinate of point $H$ is the distance of point $H$ from the $x$ -axis. Therefore, the ordinate of point $H$ is $-3$.

vii) The coordinates of the point \[L\].

Ans: In the Figure, the coordinates of point \[L\] is the distance of point \[L\] from $x$ -axis and $y$ -axis. Therefore, the coordinates of point \[L\] are \[(0,5)\].

viii) The coordinates of the point \[M\].

Ans: In the Figure, the coordinates of point \[M\] is the distance of point \[M\] from $x$ -axis and $y$-axis. Therefore, the coordinates of point \[M\] are \[(-3,0)\].

Exercise 3.3

1. In which quadrant or on which axis do each of the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0)},\text{ (1,2)}\] and \[(-3,-5)\] lie? Verify your answer by locating them on the Cartesian plane.

Ans: We have to get the quadrant or axis of the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0)}\] , \[(1,2)\] and \[(-3,-5)\].

First, plot the plot the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0),}\ (1,2)\] and \[(-3,-5)\] on the graph, to get,

From the Figure given above, we can say that the points

\[(-2,4)\]  lie in \[IInd\] quadrant.

\[(3,-1)\]  lie in \[IVth\] quadrant.

\[(-1,0)\]  lie on the negative $x$ - axis.

\[(1,2)\]  lie in \[Ist\] quadrant.

\[(-3,-5)\]  lie in \[IIIrd\] quadrant

2. Plot the points \[\left( x,\text{ }y \right)\] given in the following table on the plane, choosing suitable units of distance on the axes.

Ans: Given,

First of all, draw \[X'OX\]  and \[Y'OY\]  as the coordinate axes and mark their point of intersection $O$ as the Origin \[\left( 0,\text{ }0 \right)\].

Then stay at origin.

To plot the points given in the above table,

Point \[A(-2,8)\] 

Move \[2\] units on \[OX'\] and then \[8\] units parallel to \[OY\]

Point \[B(-1,7)\]

Move -1 unit on \[OX'\] and then \[7\] units parallel to \[OY\]

Point \[C(0,-1.25)\],

Move \[1.25\] units below x-axis on \[OY'\] on the y-axis

Point \[D(1,3)\] 

Move \[1\] unit on \[OX\] and then \[3\] units parallel to \[OY\]

Point \[E(3,-1)\],

Move \[3\] units on \[OX\] and then move \[1\]  unit parallel to \[OY'\].

Chapter-wise Class 9 Maths NCERT Solutions Free PDF

Apart from NCERT Solutions for Class 9 Maths Chapter 3, you can also download the free PDFs of NCERT Solutions for the following chapters covered in NCERT Class 9 Maths textbook.

• Chapter 1 - Number System

• Chapter 2 - Polynomials 

• Chapter 3 - Coordinate Geometry

• Chapter 4 - Linear Equations in Two Variables

• Chapter 5 - Introductions to Euclid Geometry

• Chapter 6 - Lines and Angles

• Chapter 7 - Triangles

• Chapter 8 - Quadrilaterals

• Chapter 9 - Areas of Parallelogram and Triangles

• Chapter 10 - Circles

• Chapter 11 - Constructions

• Chapter 12 - Heron's formula

• Chapter 13 - Surface area and Volumes

• Chapter 14 - Statistics

• Chapter 15 - Probability

NCERT Class 9 Chapter 3 Coordinate Geometry Solutions: Summary

Class 9 Chapter 3 Maths will introduce you to Cartesian coordinates. Here you will find a 2D world with two axes, ‘X’ and ‘Y’. Any point can be plotted on this plane using the coordinates and hints. As the chapter proceeds, the exercises provide a platform where you can judge your level of understanding of the concepts. You will have to solve all the questions prescribed in every exercise to develop your concepts well. This is where you will need the NCERT Solutions for Class 9 Maths Chapter 3 to clear your doubts and build a strong foundation that will help you learn higher concepts later.

Class 9 Maths Chapter 3 Solutions have been composed by expert teachers so that you will find your confusion cleared in a moment. The teachers know students' common problems while solving problems in the exercises of Chapter 3 Maths Class 9. Once you finish the classes, you can proceed to the exercise part and start solving the questions. You will discover how efficiently NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry has addressed the problems you faced while solving the exercises.

Follow the techniques used by the teachers and learn how to approach a coordinate geometry problem efficiently. Download the NCERT Solutions for Class 9 Maths Coordinate Geometry and get the best support from the top maths teachers.

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Extra Questions for Practice

1. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively. Note:  One of the vertices of the rectangle is at the origin, the longer side lies on the x-axis, and one of the vertices lies in the third quadrant.

2. Locate the following points in the Cartesian plane.

(5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and (6, 1).

3. Solve the following equations:

(i) 3x + 3 = 15

(ii) 2y + 7 =19

Get NCERT Class 9 Maths Chapter 3 Solutions and make sure your knowledge base of coordinate geometry becomes stronger. Refer to the intelligent yet simple answers to the exercise questions of Class 9th Maths Chapter 3 and understand the concepts well.

Conclusion 

NCERT Solutions for Class 9 Maths Chapter 3 - Coordinate Geometry provide a comprehensive and detailed understanding of the fundamental concepts of coordinate geometry. This chapter introduces students to the Cartesian coordinate system and its applications in representing points and geometric shapes in a two-dimensional plane. The solutions begin by explaining the basics of coordinates, plotting points, and understanding the four quadrants of the coordinate plane. Students learn how to identify the coordinates of a point and how to plot points based on given coordinates. Moreover, NCERT Solutions for Class 9 Maths Chapter 3 delve into the concept of the distance formula, enabling students to calculate the distance between two points on the coordinate plane. They also explore the concept of the section formula, which helps in dividing a line segment into a given ratio.