CBSE Class 9 Maths Chapter 3 Coordinate Geometry NCERT Solutions

Reviewed by · Updated on

NCERT Solutions PDF Class 9 PDF

This chapter provides essential NCERT Solutions for Class 9 Maths, focusing on Coordinate Geometry. Students will learn to identify the location of points based on their coordinates in a Cartesian plane. The solutions cover understanding quadrants, the signs of coordinates in each quadrant, points on the axes, and the significance of the origin. Key concepts like abscissa (x-coordinate) and ordinate (y-coordinate) are explained. These solutions are designed to clarify the fundamental principles of plotting points and interpreting their positions, aiding students in mastering this foundational topic for their exams.

Home

Quick info

BoardCBSE
ClassClass 9
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3

Chapter summary

Chapter 3, Coordinate Geometry, introduces students to the Cartesian coordinate system. These NCERT Solutions explain how to determine the quadrant or axis on which a point lies based on the signs and values of its coordinates. It covers the definitions of origin, abscissa, and ordinate, and their properties concerning points on the axes. The exercises focus on identifying the correct location of points like (-3, 5), (0, -7), (-10, 0), and points with negative coordinates.

Learning outcomes

  • Understand the Cartesian coordinate system and its components.
  • Identify the quadrant in which a point lies based on its coordinates.
  • Determine if a point lies on the x-axis or y-axis.
  • Define and identify the origin, abscissa, and ordinate.
  • Interpret the signs of coordinates for points in different quadrants.

Topics covered

Paper topics

  • Coordinate Geometry
  • Cartesian Coordinate System
  • Plotting Points
  • Quadrants
  • Axes (x-axis, y-axis)
  • Origin
  • Abscissa
  • Ordinate
  • Signs of Coordinates
  • Points on Axes

Important topics

  • Identifying Quadrants
  • Points on Axes
  • Definition of Origin, Abscissa, Ordinate
  • Sign Conventions in Quadrants

PDF preview

Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.

Loading document …
Page of
Loading page …

Questions and Solutions

Question 1

Write the correct answer in each of the following: Point <math>(-3, 5)</math> lies in the
  1. first quadrant
  2. second quadrant
  3. third quadrant
  4. fourth quadrant
Solution: The given point is <math>(-3, 5)</math>. In this point, the x-coordinate (abscissa) is -3, which is negative, and the y-coordinate (ordinate) is 5, which is positive. According to the sign conventions for the Cartesian plane, a point with a negative abscissa and a positive ordinate lies in the second quadrant. Therefore, the correct option is (B) second quadrant.

Question 2

Signs of the abscissa and ordinate of a point in the second quadrant are respectively
  1. <math>(A) +, +</math>
  2. <math>(B) -, -</math>
  3. <math>(C) -, +</math>
  4. <math>(D) +, -</math>
Solution: The Cartesian plane is divided into four quadrants. In the first quadrant, both coordinates are positive (+, +). In the second quadrant, the x-coordinate (abscissa) is negative, and the y-coordinate (ordinate) is positive (-, +). In the third quadrant, both coordinates are negative (-, -). In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative (+, -). Therefore, for a point in the second quadrant, the signs of the abscissa and ordinate are respectively negative and positive. The correct option is (C).

Question 3

Point <math>(0, -7)</math> lies
  1. on the x –axis
  2. in the second quadrant
  3. on the y-axis
  4. in the fourth quadrant
Solution: The given point is <math>(0, -7)</math>. A point lies on the x-axis if its y-coordinate (ordinate) is 0. A point lies on the y-axis if its x-coordinate (abscissa) is 0. Since the x-coordinate of the point (0, -7) is 0, it lies on the y-axis. Specifically, because the y-coordinate is negative, it lies on the negative part of the y-axis. Therefore, the correct option is (C) on the y-axis.

Question 4

Point (-10, 0) lies
  1. on the negative direction of the x-axis
  2. on the negative direction of the y-axis
  3. in the third quadrant
  4. in the fourth quadrant
Solution: The given point is (-10, 0). A point lies on the x-axis if its y-coordinate (ordinate) is 0. A point lies on the y-axis if its x-coordinate (abscissa) is 0. Since the y-coordinate of the point (-10, 0) is 0, it lies on the x-axis. Furthermore, because the x-coordinate is -10, which is negative, the point lies on the negative direction of the x-axis. Therefore, the correct option is (A).

Question 5

Abscissa of all the points on the x-axis is
  1. 0
  2. 1
  3. 2
  4. any number
Solution: The x-axis is defined as the set of all points where the y-coordinate (ordinate) is 0. The x-coordinate (abscissa) can be any real number, representing the horizontal position along the axis. For example, points like (5, 0), (-2, 0), and (0, 0) are all on the x-axis. Therefore, the abscissa of all points on the x-axis can be any number. The correct option is (D).

Question 6

Ordinate of all points on the x-axis is
  1. 0
  2. 1
  3. - 1
  4. any number
Solution: The x-axis is a horizontal line passing through the origin. Any point located on the x-axis has a vertical distance of zero from the x-axis itself. This means that the y-coordinate, also known as the ordinate, is always 0 for any point on the x-axis. For instance, points like (3, 0), (-7, 0), and (0, 0) all have an ordinate of 0. Therefore, the correct option is (A).

Question 7

The point at which the two coordinate axes meet is called the
  1. abscissa
  2. ordinate
  3. origin
  4. quadrant
Solution: The two coordinate axes, the horizontal x-axis and the vertical y-axis, intersect at a single point. This specific point is known as the origin. The coordinates of the origin are always (0, 0), representing the starting point for measuring distances along both axes. Therefore, the correct option is (C) origin.

Question 8

A point both of whose coordinates are negative will lie in
  1. I quadrant
  2. II quadrant
  3. III quadrant
  4. IV quadrant
Solution: In the Cartesian coordinate system, the quadrants are defined by the signs of the coordinates. Quadrant I has positive x and positive y (+, +). Quadrant II has negative x and positive y (-, +). Quadrant III has negative x and negative y (-, -). Quadrant IV has positive x and negative y (+, -). A point where both coordinates are negative, meaning both the abscissa and the ordinate are negative, will therefore lie in the III quadrant. The correct option is (C).

Question 9

Points <math>(1, -1)</math>, <math>(2, -2)</math>, <math>(4, -5)</math>, <math>(-3, -4)</math>
Solution: This question appears incomplete as it lists points without asking a specific question about them. However, we can analyze the location of each point:
  • <math>(1, -1)</math>: x is positive, y is negative. This point lies in the IV quadrant.
  • <math>(2, -2)</math>: x is positive, y is negative. This point also lies in the IV quadrant.
  • <math>(4, -5)</math>: x is positive, y is negative. This point lies in the IV quadrant.
  • <math>(-3, -4)</math>: x is negative, y is negative. This point lies in the III quadrant.
If the question intended to ask where these points lie, then (1, -1), (2, -2), and (4, -5) are in the fourth quadrant, while (-3, -4) is in the third quadrant. Without a specific question, a definitive answer cannot be provided.

Common mistakes

  • Confusing the signs of coordinates for different quadrants (e.g., mixing up Quadrant II and Quadrant IV).
  • Incorrectly identifying points on the axes (e.g., thinking (0, -7) is on the x-axis).
  • Confusing abscissa and ordinate.
  • Not recognizing that the ordinate of any point on the x-axis is zero.

Revision tips

  • Draw a Cartesian plane and plot sample points to visualize quadrant locations.
  • Memorize the sign conventions for coordinates in each of the four quadrants.
  • Practice identifying points on the x-axis and y-axis, paying attention to zero coordinates.
  • Review the definitions of origin, abscissa, and ordinate thoroughly.

Practice MCQs

Q1. In which quadrant does the point (-3, 5) lie?

Q2. What are the signs of the abscissa and ordinate of a point in the second quadrant, respectively?

Q3. The point (0, -7) lies on which axis?

Q4. The point (-10, 0) lies on which part of the coordinate plane?

Q5. What is the value of the abscissa for all points lying on the x-axis?

Q6. What is the value of the ordinate for all points lying on the x-axis?

Q7. What is the name of the point where the x-axis and y-axis intersect?

Q8. A point where both coordinates are negative will be located in which quadrant?

Frequently asked questions

What is Coordinate Geometry?

Coordinate Geometry is a branch of mathematics that uses a coordinate system to represent and analyze geometric figures. It establishes a link between algebra and geometry by using ordered pairs of numbers (coordinates) to locate points on a plane.

How do I determine which quadrant a point lies in?

Observe the signs of the coordinates. If both are positive, it's Quadrant I. If the x-coordinate is negative and y-coordinate is positive, it's Quadrant II. If both are negative, it's Quadrant III. If the x-coordinate is positive and y-coordinate is negative, it's Quadrant IV.

What is the difference between abscissa and ordinate?

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

Where do points with a zero coordinate lie?

If the x-coordinate is zero (e.g., (0, 5)), the point lies on the y-axis. If the y-coordinate is zero (e.g., (-10, 0)), the point lies on the x-axis.

What is the origin in the coordinate system?

The origin is the point where the x-axis and y-axis intersect. Its coordinates are always (0, 0).

How can these NCERT solutions help with exam preparation?

These solutions provide clear, step-by-step explanations for each question, reinforcing understanding of fundamental concepts like quadrants, axes, and coordinate signs, which are crucial for exam success.

Important links

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.