CBSE · Class 9 · Mathematics · Chapter 3

Coordinate
Geometry

Complete chapter resources for CBSE Class 9 Mathematics — topic breakdown, key formulas, sample questions, previous year board questions, and instant AI question paper generation.

3Topics
4–6Board marks
8Sample questions
3PYQ included
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Key Formulas — Chapter 3
  • Ordered pair: Point P = (x, y) where x = abscissa, y = ordinate
  • Origin: O = (0, 0) — intersection of axes
  • Distance formula: d = √((x₂−x₁)² + (y₂−y₁)²)
  • Distance from origin: d = √(x² + y²)
  • Quadrants: I(+,+) II(−,+) III(−,−) IV(+,−)
  • Collinearity check: AB + BC = AC (three points)
Chapter Overview

What this chapter covers

Coordinate Geometry introduces the Cartesian plane — a two-dimensional grid formed by two perpendicular number lines called the x-axis (horizontal) and y-axis (vertical). Their point of intersection is the origin, denoted O(0, 0). Every point in the plane is uniquely described by an ordered pair (x, y), where x is the abscissa (horizontal distance from the y-axis) and y is the ordinate (vertical distance from the x-axis).

The plane is divided into four quadrants by the axes. Moving anti-clockwise from the positive x-axis: Quadrant I has both coordinates positive (+, +), Quadrant II has x negative and y positive (−, +), Quadrant III has both negative (−, −), and Quadrant IV has x positive and y negative (+, −). Points lying exactly on an axis belong to no quadrant and carry a zero in one coordinate.

The chapter also covers the distance formula — d = √((x₂ − x₁)² + (y₂ − y₁)²) — derived from the Pythagorean theorem. Board questions apply this formula to determine whether three points are collinear, form a specific triangle type, or are equidistant from the origin. This formula is a prerequisite for the Section Formula and Mid-Point theorem covered in Class 10.

Topics

What's inside Chapter 3

As per NCERT Class 9 Mathematics (CBSE syllabus)

Topic 1
The Cartesian Plane & Coordinate Axes
Introduction to the x-axis, y-axis, and origin. Naming the four quadrants and identifying where a point lies based on the signs of its coordinates. Points on the axes carry one zero coordinate.
Topic 2
Plotting Points & Reading Coordinates
Locating points of the form (x, y) on the Cartesian plane by moving x units along the horizontal axis and y units vertically. Reading the coordinates of a plotted point and distinguishing abscissa from ordinate.
Topic 3
Distance Between Two Points
Deriving and applying the distance formula d = √((x₂−x₁)² + (y₂−y₁)²). Uses include verifying collinearity of three points, classifying triangles by side lengths, and checking whether points form geometric shapes.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 8 · Number Line
Representing integers and rationals on a single axis
Ch 6 · Lines & Angles (Class 9)
Perpendicular lines and angle properties of intersecting lines
Chapter 3 Coordinate
Geometry
Leads to
Class 10 · Coordinate Geometry
Section formula, mid-point formula, area of a triangle
Class 11 · Straight Lines
Slope, equations of lines, locus problems in the coordinate plane
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 9 annual and SA papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1–2 Quadrant identification, sign of coordinates, or axis position
Very Short Answer 2 1 Plot a point, name coordinates, or identify abscissa / ordinate
Short Answer 3 1 Distance between two points or verify collinearity of three points
Long Answer 4 0–1 Classify a triangle or quadrilateral by computing all relevant distances
Total (approximate) 4–6 3–4 Weightage varies across school papers and exam terms
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 9 Maths Chapter 3. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The point (−3, 5) lies in which quadrant of the Cartesian plane? (a) Quadrant I (b) Quadrant II (c) Quadrant III (d) Quadrant IV
Q2 Easy 2 marks Short Answer
Write the coordinates of a point that lies on the negative y-axis at a distance of 7 units from the origin. Also state the quadrant it belongs to.
Q3 Medium 2 marks Short Answer
Find the distance between the points A(3, 4) and B(−1, 1) using the distance formula.
Q4 Medium 2 marks Short Answer
A point P lies on the x-axis and is equidistant from the points A(2, 3) and B(6, −3). Find the coordinates of P.
Q5 Medium 3 marks Short Answer
Show that the points A(1, 1), B(4, 4), and C(7, 7) are collinear using the distance formula.
Q6 Hard 4 marks Word Problem
The vertices of a triangle are P(2, 1), Q(6, 1), and R(4, 5). Using the distance formula: (i) Find the lengths of all three sides. (ii) Determine what type of triangle PQR is (scalene, isosceles, or equilateral).
Q7 Hard 4 marks Word Problem
A delivery drone starts at the origin O(0, 0), flies to station A(6, 0), then to station B(6, 8), and finally returns to O. (i) Find the total distance covered by the drone. (ii) Find the straight-line distance from A to O directly after the final leg. (iii) Verify your answer for leg OA using the distance formula.
Q8 Hard 5 marks Case-Based
A school plans a garden in a coordinate grid where each unit = 1 metre. The four corners of the garden are at A(1, 1), B(7, 1), C(7, 5), and D(1, 5). (i) Plot the four points (description only — name coordinates for each). (ii) Calculate the length and breadth of the garden using the distance formula. (iii) Find the diagonal AC and verify it equals the diagonal BD. (iv) What shape is ABCD? Justify using the side lengths and diagonals.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 9 Maths papers — Coordinate Geometry chapter.

Board 20222 marks
In which quadrant or on which axis do each of the following points lie? (i) (−2, 4)   (ii) (3, −1)   (iii) (−5, 0)   (iv) (2, 7). (CBSE SA1 2022)
Board 20233 marks
Using the distance formula, show that the points A(5, 6), B(1, 5), C(2, 1), and D(6, 2) are the vertices of a square. (CBSE Annual 2023)
Board 20202 marks
Find the distance between the points (0, 0) and (36, 15). Is the answer a rational number? Justify. (CBSE SA1 2020)
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FAQ

Questions teachers ask

How many marks does Coordinate Geometry carry in the CBSE Class 9 annual exam? +
Coordinate Geometry typically carries 4–6 marks in the CBSE Class 9 annual examination. Expect one 1-mark objective question on quadrant identification or axis position, one 2-mark question on plotting or naming coordinates, and occasionally a 3-mark question asking students to find the distance between two given points. The exact distribution varies by school and paper set.
What is the Cartesian plane and how are quadrants numbered in CBSE Class 9? +
The Cartesian plane is formed by two perpendicular number lines — the horizontal x-axis and the vertical y-axis — intersecting at the origin (0, 0). The plane is divided into four quadrants numbered anti-clockwise from the positive x-axis: Quadrant I (+, +), Quadrant II (−, +), Quadrant III (−, −), and Quadrant IV (+, −). Points on an axis belong to no quadrant.
Is the distance formula part of the CBSE Class 9 Coordinate Geometry syllabus? +
Yes. The NCERT Class 9 Chapter 3 introduces the distance formula: d = √((x₂−x₁)² + (y₂−y₁)²). Students are expected to use it to find the distance between two points and to determine whether three given points are collinear, form a right triangle, or are equidistant from a fixed point. It is a high-probability 2–3 mark question in most annual papers.
What is the difference between abscissa and ordinate? +
In the ordered pair (x, y), the abscissa is the x-coordinate (horizontal distance from the y-axis) and the ordinate is the y-coordinate (vertical distance from the x-axis). Board questions frequently ask students to identify, compare, or swap these values — for example, "find the point whose ordinate equals its abscissa" — making this distinction a common 1-mark target.
How do I generate a custom question paper for Coordinate Geometry using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 9 Mathematics, select Chapter 3 (Coordinate Geometry), set your preferred question-type mix (MCQ, short answer, word problem) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.