CBSE Class 9 Maths Chapter 3: Coordinate Geometry NCERT Solutions

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NCERT Solutions PDF Class 9 PDF

This chapter introduces students to the fundamental concepts of Coordinate Geometry, a crucial branch of mathematics. The NCERT Solutions for Class 9 Maths Chapter 3 cover how to describe the position of objects in a plane using coordinates. It explains the Cartesian coordinate system, including the x-axis, y-axis, origin, and quadrants. The solutions provide step-by-step guidance on plotting points, identifying coordinates, and understanding the significance of abscissa and ordinate. These solutions are designed to help students grasp the basics of locating points on a plane, which is essential for further mathematical studies and applications in various fields. They serve as an excellent resource for exam preparation, offering clarity and practice on key concepts.

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BoardCBSE
ClassClass 9
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3: Coordinate Geometry

Chapter summary

Chapter 3: Coordinate Geometry for Class 9 NCERT Solutions focuses on introducing the Cartesian coordinate system. It covers defining the position of a point using ordered pairs, understanding the roles of the horizontal (x-axis) and vertical (y-axis) lines, the intersection point (origin), and the four regions (quadrants) they create. The solutions provide practice in identifying coordinates of points and plotting points given their coordinates, using examples like a street plan and a graph.

Learning outcomes

  • Understand the concept of describing the position of an object using a coordinate system.
  • Identify and define the x-axis, y-axis, origin, and quadrants in a Cartesian plane.
  • Determine the coordinates of a point given its location on the plane.
  • Plot points on the Cartesian plane given their coordinates.
  • Differentiate between the abscissa and ordinate of a point.

Topics covered

Paper topics

  • Introduction to Coordinate Geometry
  • Cartesian Coordinate System
  • x-axis
  • y-axis
  • Origin
  • Quadrants
  • Coordinates of a Point
  • Plotting Points
  • Abscissa
  • Ordinate
  • Describing Position

Important topics

  • Cartesian Coordinate System
  • Plotting Points
  • Identifying Coordinates
  • Quadrants and Axes
  • Origin

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Questions and Solutions

Question 1

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

To describe the position of the table lamp on your study table, you need a reference point and two perpendicular directions. Imagine your study table as a plane. You can choose one corner of the table as the origin (0,0). Then, you can measure the distance of the lamp along two perpendicular edges of the table. For example, if the lamp is 2 feet away from the edge closest to you (say, along the length) and 1 foot away from the right edge (say, along the width), you can describe its position as (2, 1). Here, the first value (2 feet) represents the distance along one direction (e.g., length), and the second value (1 foot) represents the distance along the perpendicular direction (e.g., width).

Answer: The position of the lamp can be described using coordinates, for instance, as (2, 1), indicating its distance from two perpendicular edges of the table.

Question 2

(Street Plan): A city has two main roads which cross each other at the centre 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 m apart. There are about 5 streets in each direction. Using 1 \text{ cm} = 200 \text{ m}, draw a model of the city on 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 (2, 5). Using this convention, find:
  1. How many cross-streets can be referred to as (4,3)?
  2. How many cross-streets can be referred to as (3, 4)?
Solution:

In this model, we can consider the North-South streets as vertical lines and the East-West streets as horizontal lines. The intersection of a North-South street and an East-West street forms a cross-street. The convention given is that a cross-street is referred to by an ordered pair (x, y), where 'x' represents the number of the street running in the North-South direction and 'y' represents the number of the street running in the East-West direction.

1. How many cross-streets can be referred to as (4, 3)?

The coordinate (4, 3) uniquely identifies a single intersection point. This means the 4th street running in the North-South direction intersects with the 3rd street running in the East-West direction. There is only one such specific intersection.

2. How many cross-streets can be referred to as (3, 4)?

Similarly, the coordinate (3, 4) uniquely identifies another specific intersection point. This refers to the 3rd street running in the North-South direction intersecting with the 4th street running in the East-West direction. There is only one such specific intersection.

It is important to note that the order of the numbers matters. The cross-street (4, 3) is different from the cross-street (3, 4).

Answer:

  1. Only one cross-street can be referred to as (4, 3).
  2. Only one cross-street can be referred to as (3, 4).

Question 1

Write the answer of each of the following questions: (i) What is the name of the horizontal and the vertical lines 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? (iii) Write the name of the point where these two lines intersect.
Solution:

The Cartesian coordinate system is used to define the position of any point in a plane using two perpendicular lines.

(i) The horizontal line is called the x-axis, and the vertical line is called the y-axis.

(ii) These two lines divide the plane into four regions, and each part is called a quadrant.

(iii) The point where the x-axis and y-axis intersect is called the origin.

Question 2

See Fig. and write the following: (i) The coordinates of B. (ii) The coordinates of C. (iii) The point identified by the coordinates (-3, -5). (iv) The point identified by the coordinates (2, -4). (v) The abscissa of the point D. (vi) The ordinate of the point H. (vii) The coordinates of the point L. (viii) The coordinates of the point M.
Solution:

We use the given figure, which shows points plotted on a Cartesian plane, to determine the answers.

(i) To find the coordinates of point B, we look at its position relative to the x-axis and y-axis. Point B is 5 units to the left of the y-axis (so its x-coordinate is -5) and 2 units above the x-axis (so its y-coordinate is 2). Thus, the coordinates of B are (-5, 2).

(ii) For point C, it is 5 units to the right of the y-axis (x-coordinate is 5) and 5 units below the x-axis (y-coordinate is -5). Thus, the coordinates of C are (5, -5).

(iii) The coordinates (-3, -5) indicate a point that is 3 units to the left of the y-axis and 5 units below the x-axis. Locating this on the graph, we find it corresponds to point E.

(iv) The coordinates (2, -4) indicate a point that is 2 units to the right of the y-axis and 4 units below the x-axis. Locating this on the graph, we find it corresponds to point G.

(v) The abscissa of a point is its x-coordinate. For point D, which is located at (6, 5), the abscissa is 6.

(vi) The ordinate of a point is its y-coordinate. For point H, which is located at (-5, -3), the ordinate is -3.

(vii) Point L is located on the y-axis. Points on the y-axis have an x-coordinate of 0. Point L is 5 units above the x-axis, so its y-coordinate is 5. Thus, the coordinates of L are (0, 5).

(viii) Point M is located on the x-axis. Points on the x-axis have a y-coordinate of 0. Point M is 3 units to the left of the y-axis, so its x-coordinate is -3. Thus, the coordinates of M are (-3, 0).

Answer:

(i) (-5, 2) (ii) (5, -5) (iii) E (iv) G (v) 6 (vi) -3 (vii) (0, 5) (viii) (-3, 0)

Common mistakes

  • Confusing the order of coordinates (x, y) vs (y, x).
  • Incorrectly identifying the quadrant a point lies in.
  • Misinterpreting the origin or axes on a graph.
  • Errors in plotting points, especially with negative coordinates.

Revision tips

  • Practice plotting points in all four quadrants.
  • Clearly label the x-axis, y-axis, and origin on every graph.
  • Review the definitions of abscissa and ordinate.
  • Use the street plan example to visualize coordinate pairs.

Practice MCQs

Q1. What is the name of the horizontal line in the Cartesian coordinate system?

Q2. What is the point of intersection of the x-axis and y-axis called?

Q3. In the coordinate pair (a, b), what does 'b' represent?

Q4. A point lies on the negative x-axis. What are its coordinates?

Q5. Which quadrant is the point (-3, 4) located in?

Frequently asked questions

What is Coordinate Geometry?

Coordinate Geometry is a branch of mathematics that uses a coordinate system to represent geometric shapes and figures algebraically. It allows us to study geometry using coordinates and equations.

What are the main components of the Cartesian coordinate system?

The main components are the x-axis (horizontal line), the y-axis (vertical line), their intersection point called the origin (0,0), and the four regions formed by these axes called quadrants.

How do you describe the position of a point in the Cartesian plane?

The position of a point is described by an ordered pair of numbers (x, y), called coordinates. The first number (x) is the distance from the y-axis (abscissa), and the second number (y) is the distance from the x-axis (ordinate).

What is the difference between abscissa and ordinate?

The abscissa is the x-coordinate, representing the horizontal position of a point. The ordinate is the y-coordinate, representing the vertical position of a point.

How can these NCERT Solutions help in exam preparation?

These solutions provide clear, step-by-step explanations for each question in the exercise, helping students understand the concepts and methods required to solve problems related to coordinate geometry for their exams.

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