NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

• 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.

Access NCERT Solutions for Class 9 Maths 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 \[(-3,0)\].

Overview of Deleted Syllabus for CBSE Class 9 Maths Coordinate Geometry

Class 9 Maths Chapter 3: Exercises Breakdown

Conclusion

NCERT Solutions for Coordinate Geometry class 9  provides 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. In previous years exams, around 2-3 questions have been asked from this chapter. NCERT Solutions for Ch 3 maths class 9 delves into the concept of the distance formula, enabling Students to calculate the distance between two points on the coordinate plane. 

Other Study Material for CBSE Class 9 Maths Chapter 3

Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

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