📐 CBSE · Class 10 · Mathematics · Chapter 7

Coordinate
Geometry

Complete chapter resources for CBSE Class 10 Maths — topic breakdown, key formulas, sample questions, previous year board questions, and instant AI question paper generation.

3Topics
6–8Board marks
8Sample questions
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Key Formulas — Chapter 7
  • Distance Formula: d = √[(x₂−x₁)² + (y₂−y₁)²]
  • Section Formula: P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
  • Midpoint Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
  • Area of Triangle: ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
  • Collinearity: Area = 0 ⟹ points are collinear
Chapter Overview

What this chapter covers

Coordinate Geometry connects algebra and geometry by representing points, lines, and shapes on the Cartesian plane using ordered pairs (x, y). Chapter 7 begins with the Distance Formula — derived from the Pythagorean theorem — which calculates the straight-line distance between any two points P(x₁, y₁) and Q(x₂, y₂) as d = √[(x₂ − x₁)² + (y₂ − y₁)²]. A key application is verifying the type of a triangle or quadrilateral by comparing side lengths.

The Section Formula extends this by finding the coordinates of a point that divides a line segment joining two given points in a specified ratio m:n (internally). When m = n, this reduces to the Midpoint Formula. Board questions frequently present a point on a segment and ask students to determine the ratio, requiring them to set up and solve the section formula for the unknown.

The chapter concludes with the Area of a Triangle using coordinates: Area = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Setting this expression equal to zero is the standard method to prove that three points are collinear. Board papers reliably include a 4-mark question on area or collinearity, making this the highest-yield topic in the chapter.

Topics

What's inside Chapter 7

As per NCERT Class 10 Mathematics (CBSE syllabus)

Topic 1
Distance Formula
Finding the distance between two points using d = √[(x₂−x₁)² + (y₂−y₁)²]. Applications include verifying triangle types (scalene, isosceles, equilateral) and quadrilateral types (parallelogram, rhombus, square) by comparing side and diagonal lengths.
Topic 2
Section Formula & Midpoint Formula
Finding the coordinates of the point that divides a segment internally in the ratio m:n using ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). The midpoint formula ((x₁+x₂)/2, (y₁+y₂)/2) is the m = n = 1 special case.
Topic 3
Area of a Triangle & Collinearity
Computing the area of a triangle with given vertices using the coordinate formula. Setting area = 0 proves collinearity of three points. This topic covers the highest-mark board questions in Chapter 7.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Class 9 · Coordinate Geometry
Cartesian plane, plotting points, quadrants, axes
Class 10 · Ch 6 · Triangles
Properties of triangles used in distance and area problems
Chapter 7 Coordinate
Geometry
Leads to
Class 11 · Straight Lines
Slope, equations of lines, distance from a point to a line
Class 11 · Conic Sections
Circles, parabolas, ellipses defined by coordinate equations
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 10 board papers from the last five years.

Question type Marks Typical count What's usually tested
MCQ / Objective 1 1–2 Distance between two points, midpoint coordinates, or ratio identification
Very Short Answer 2 1 Apply distance formula to verify a geometric shape or find a missing coordinate
Short Answer 3 1 Section formula to find a dividing point, or prove collinearity using area = 0
Long Answer / Application 4–5 1 Area of a triangle / quadrilateral given vertices, or multi-step geometry proof
Total (approximate) 6–8 4–5 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 10 Maths Chapter 7. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The distance between the points A(2, 3) and B(−1, 7) is: (a) 3 (b) 4 (c) 5 (d) 7
Q2 Easy 2 marks Short Answer
Find the midpoint of the line segment joining P(−3, 5) and Q(7, −1).
Q3 Medium 2 marks Short Answer
Find the coordinates of the point which divides the line segment joining A(1, 3) and B(4, 9) in the ratio 2:1 internally.
Q4 Medium 3 marks Short Answer
Using the distance formula, show that the points A(1, −2), B(3, 6), C(5, 10) are collinear.
Q5 Medium 3 marks Short Answer
In what ratio does the point (3, 4) divide the line segment joining A(1, 2) and B(6, 7)? Also verify your answer.
Q6 Hard 4 marks Word Problem
The vertices of a triangle are A(2, 1), B(−2, 3), and C(4, 5). Find the area of triangle ABC and check whether it is a right-angled triangle using the distance formula.
Q7 Hard 4 marks Word Problem
The four vertices of a quadrilateral are A(1, 1), B(7, −3), C(12, 2), D(7, 21). Using the distance formula and the midpoint formula, determine whether ABCD is a parallelogram.
Q8 Hard 5 marks Case-Based
A park authority places three water fountains at coordinates F₁(0, 0), F₂(4, 0), and F₃(4, 3). (i) Find the distances F₁F₂, F₂F₃, and F₁F₃. (ii) Prove that the three fountains form a right-angled triangle. (iii) Find the coordinates of the point where a maintenance path from F₁ meets the midpoint of F₂F₃. (iv) Calculate the area enclosed by the three fountains.
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 10 Maths board papers — Coordinate Geometry chapter.

Board 20222 marks
Find the ratio in which the line segment joining the points A(6, 3) and B(−3, −7) is divided by the x-axis. (All India 2022)
Board 20233 marks
Show that the points A(1, 2), B(5, 4), C(3, 8), D(−1, 6) are the vertices of a square. (Delhi 2023)
Board 20204 marks
If A(−2, 1), B(a, 0), C(4, b), and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of the sides of the parallelogram. (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Coordinate Geometry carry in the CBSE Class 10 board exam? +
Coordinate Geometry typically carries 6–8 marks in the CBSE Class 10 Maths board exam, spread across 2–4 questions. Expect one 1-mark MCQ on the distance or section formula, one 2-mark short answer, and one 4-mark application question involving the area of a triangle or collinearity of three points.
What is the Distance Formula and how is it derived? +
The Distance Formula gives the length between two points P(x₁, y₁) and Q(x₂, y₂) as d = √[(x₂ − x₁)² + (y₂ − y₁)²]. It is derived directly from the Pythagorean theorem by treating the horizontal and vertical gaps between the two points as legs of a right-angled triangle. CBSE board questions test both the formula application and its derivation.
When do students use the Section Formula versus the Midpoint Formula? +
The Section Formula — ((m·x₂ + n·x₁)/(m+n), (m·y₂ + n·y₁)/(m+n)) — is used when a point divides a line segment in a given ratio m:n internally. The Midpoint Formula is the special case where m = n = 1, giving ((x₁+x₂)/2, (y₁+y₂)/2). Board questions often give a point on a segment and ask for the ratio, which requires setting up and solving the section formula.
How is the area of a triangle found using coordinates in board exams? +
Given three vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃), the area is (1/2)|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. A common board question sets this area to zero to prove the three points are collinear. Always use the absolute value to avoid a negative area, and show full working for full marks.
How do I generate a custom question paper for Coordinate Geometry using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 10 Mathematics, select Chapter 7 (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.