Class 9 Maths Chapter 3 Coordinate Geometry NCERT Solutions | Complete Guide with Step-by-Step Questions

Class 9 Maths Chapter 3

Coordinate Geometry – NCERT Solutions and Concepts

Coordinate Geometry connects algebra and geometry. Instead of describing points only with diagrams, we describe them using numbers called coordinates.

In this chapter, students learn how to locate points on a plane using two perpendicular number lines. This system was introduced by the mathematician René Descartes, so it is called the Cartesian coordinate system.

Once you understand coordinates, plotting points becomes easy and many geometry problems can be solved using algebra.

Basic Terms in Coordinate Geometry

Cartesian Plane

A plane formed by two perpendicular number lines.

The horizontal line is called the x-axis.

The vertical line is called the y-axis.

Introduction

Hey, if you're tackling Class 9 CBSE Maths Chapter 3 on Coordinate Geometry, you're in the right spot. This chapter introduces the Cartesian plane, where you use x and y coordinates to locate points, just like giving directions on a map. It builds basics for graphs and geometry ahead.

You'll learn about axes, origin, quadrants, and plotting points. No fancy formulas yet – mostly understanding positions. Perfect for exams if you practice the NCERT exercises here with full solutions.

Key Formulas

This chapter keeps it simple with no heavy formulas, but remember these basics:

• Coordinates of a point: (x, y), where x is abscissa (horizontal from y-axis), y is ordinate (vertical from x-axis).
  

• Origin: (0, 0)

• Quadrants: I (+x,+y), II (-x,+y), III (-x,-y), IV (+x,-y)
  

That's it – focus on plotting accurately.

Exercise 3.1 Solved Examples

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

Solution: Imagine the table as a plane. Pick two perpendicular edges as x-axis (horizontal) and y-axis (vertical). Measure distance from y-axis (x or abscissa) and from x-axis (y or ordinate). Say the lamp is at (a, b) cm from origin.

Question 2: (Street Plan) A city has two main roads crossing at center... find cross-streets (4,3) and (3,4).

Solution: Draw grid: 1 cm = 200 m, 5 streets each way. (4,3) is unique crossing of 4th N-S and 3rd E-W street. (3,4) is 3rd N-S and 4th E-W. Each pair gives one cross-street.

Exercise 3.2 Solved Examples

Question 1: (i) Name of horizontal/vertical lines? (ii) Parts of plane? (iii) Intersection point?

Solution:
(i) Horizontal: x-axis, Vertical: y-axis.
(ii) Quadrants.
(iii) Origin.

Question 2: From figure: (i) Coords of B? (ii) C? (iii) Point (-3,-5)? etc.

Solution:
(i) B: (-5, 2)
(ii) C: (5, -5)
(iii) E
(iv) G (2, -4)
(v) Abscissa D: 6
(vi) Ordinate H: -3
(vii) L: (0, 5)
(viii) M: (-3, 0)

Exercise 3.3 Solved Examples

Question 1: Quadrant/axis for (-2,4), (3,-1), (-1,0), (1,2), (-3,-5)?

Solution:

• (-2,4): II quadrant (-x, +y)

• (3,-1): IV (+x, -y)

• (-1,0): Negative x-axis

• (1,2): I (+x, +y)

• (-3,-5): III (-x, -y)
  Plot to verify.
  

Question 2: Plot (-2,8), (-1,7), (0,-1.25), (1,3), (3,-1).

Solution: Draw axes. From origin:

• A(-2,8): left 2, up 8

• B(-1,7): left 1, up 7

• C(0,-1.25): down 1.25 on y-axis

• D(1,3): right 1, up 3

• E(3,-1): right 3, down 1
  

15 FAQs

1. What is coordinate geometry? Branch using numbers to locate points on plane.

2. Abscissa or ordinate of (3,4)? Abscissa 3, ordinate 4.
   

3. Origin coordinates? (0,0)
   

4. Point on positive y-axis? (0, positive y)
   

5. Quadrant for (4,5)? I
   

6. How plot (2,-3)? Right 2 on x, down 3 on y.
   

7. Negative x-axis point? (-ve x, 0)
   

8. (0,0) lies where? Origin.
   

9. Quadrant III signs? Both negative.
   

10. Street plan unique? Yes, ordered pair (m,n).
    ​

11. x-axis name? Horizontal line.
    

12. Quadrants count? Four.
    ​

13. Point E (-3,-5)? III quadrant.
    ​

14. Abscissa zero means? On y-axis.
    ​

15. Plot table lamp? Use distances as (x,y).
    

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