Coordinate Geometry — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Coordinate Geometry" — 9 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Coordinate Geometry" — 9 important questions with detailed answers for CBSE board…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

State the distance formula. Find the distance between points A(3, 4) and B(6,…
Find the coordinates of the point that divides the line segment joining A(2, …
Prove that the points A(0, 0), B(3, 4), and C(6, 8) are collinear.
Find the area of the triangle with vertices A(1, 2), B(4, 6), and C(5, 1).
The midpoint of a line segment joining A and B is M(2, 3). If A is (0, 1), fi…
Three vertices of a parallelogram are A(1, 2), B(4, 3), and C(6, 6). Find the…
+ 3 more questions in the full chapter

Solutions Summary:

Question	Status
State the distance formula. Find the distance between poi…	✓ Solved
Find the coordinates of the point that divides the line s…	✓ Solved
Prove that the points A(0, 0), B(3, 4), and C(6, 8) are c…	✓ Solved
Find the area of the triangle with vertices A(1, 2), B(4,…	✓ Solved
The midpoint of a line segment joining A and B is M(2, 3)…	✓ Solved
Three vertices of a parallelogram are A(1, 2), B(4, 3), a…	✓ Solved

Showing 6 of 9 questions

Q1: State the distance formula. Find the distance between points A(3, 4) and B(6, 8).

Distance Formula: The distance d between two points P(x₁, y₁) and Q(x₂, y₂) in a coordinate plane is: d = √[(x₂ - x₁)² + (y₂ - y₁)²] This formula is derived from the Pythagorean theorem. Problem: Find distance between A(3, 4) and B(6, 8) Step 1: Identify the coordinates. Point A: x₁ = 3, y₁ = 4 Point B: x₂ = 6, y₂ = 8 Step 2: Substitute into the distance formula. d = √[(6 - 3)² + (8 - 4)²] Step 3: Simplify inside the square root. d = √[(3)² + (4)²] d = √[9 + 16] d = √25 d = 5 units Answer:...

Q2: Find the coordinates of the point that divides the line segment joining A(2, 3) and B(8, 9) in the ratio 2:1 internally.

Section Formula (Internal Division): If point P divides the line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m:n, then: P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)) Given: A(2, 3), B(8, 9) Ratio = 2:1 (m:n = 2:1) Step 1: Identify the values. x₁ = 2, y₁ = 3 x₂ = 8, y₂ = 9 m = 2, n = 1 Step 2: Apply the section formula for x-coordinate. x = (m·x₂ + n·x₁)/(m + n) x = (2·8 + 1·2)/(2 + 1) x = (16 + 2)/3 x = 18/3 x = 6 Step 3: Apply the section formula for y-coordinate. y...

Q3: Prove that the points A(0, 0), B(3, 4), and C(6, 8) are collinear.

Given: Points A(0, 0), B(3, 4), C(6, 8) Prove: These points are collinear (lie on the same line) Method 1: Using Slope Step 1: Find the slope of AB. Slope of AB = (y₂ - y₁)/(x₂ - x₁) = (4 - 0)/(3 - 0) = 4/3 Step 2: Find the slope of BC. Slope of BC = (8 - 4)/(6 - 3) = 4/3 Step 3: Check if slopes are equal. Slope of AB = Slope of BC = 4/3 Also, B lies on both lines, and A and C are on the same side of B. Step 4: Conclusion. Since the slopes are equal and B is a common point, the three point...

Q4: Find the area of the triangle with vertices A(1, 2), B(4, 6), and C(5, 1).

Area of Triangle using Coordinate Formula: For a triangle with vertices A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃): Area = (1/2)|x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| Given: A(1, 2), B(4, 6), C(5, 1) x₁ = 1, y₁ = 2 x₂ = 4, y₂ = 6 x₃ = 5, y₃ = 1 Step 1: Substitute into the formula. Area = (1/2)|1(6 - 1) + 4(1 - 2) + 5(2 - 6)| Step 2: Calculate each term. = (1/2)|1(5) + 4(-1) + 5(-4)| = (1/2)|5 - 4 - 20| = (1/2)|-19| = (1/2)(19) = 9.5 square units Answer: Area of triangle ABC = 9.5 square units or...

Q5: The midpoint of a line segment joining A and B is M(2, 3). If A is (0, 1), find the coordinates of B.

Midpoint Formula: If M is the midpoint of AB where A(x₁, y₁) and B(x₂, y₂), then: M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Given: M(2, 3) is the midpoint A(0, 1) Find: B(x₂, y₂) Step 1: Apply the midpoint formula for the x-coordinate. 2 = (0 + x₂)/2 4 = 0 + x₂ x₂ = 4 Step 2: Apply the midpoint formula for the y-coordinate. 3 = (1 + y₂)/2 6 = 1 + y₂ y₂ = 5 Answer: B(4, 5) Verification: Midpoint of A(0, 1) and B(4, 5) = ((0 + 4)/2, (1 + 5)/2) = (2, 3) ✓

Q6: Three vertices of a parallelogram are A(1, 2), B(4, 3), and C(6, 6). Find the coordinates of the fourth vertex D.

Property of Parallelogram: In a parallelogram, the diagonals bisect each other. If ABCD is a parallelogram with diagonals AC and BD, then the midpoint of AC equals the midpoint of BD. Given: A(1, 2), B(4, 3), C(6, 6) Find: D(x, y) Assuming the vertices are in order A, B, C, D: Step 1: Find the midpoint of diagonal AC. Midpoint of AC = ((1 + 6)/2, (2 + 6)/2) = (7/2, 4) = (3.5, 4) Step 2: This midpoint must equal the midpoint of diagonal BD. Midpoint of BD = ((4 + x)/2, (3 + y)/2) Step 3: Set...

Showing 6 of 9 questions. Visit the full page for complete solutions.