MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 25

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerCoordinate Geometry

Using distance formula, prove that the points $(1, 5)$ , $(2, 3)$ and $(3, 1)$ are collinear.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Three points are collinear if the sum of two of the distances equals the third.

Hint 2

Use $d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ for AB, BC and AC.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Let A(1, 5), B(2, 3), C(3, 1).
$A B = (2 - 1)^{2} + (3 - 5)^{2} = 1 + 4 = 5$
½ mark
$B C = (3 - 2)^{2} + (1 - 3)^{2} = 1 + 4 = 5$
½ mark
$A C = (3 - 1)^{2} + (1 - 5)^{2} = 4 + 16 = 20 = 25$
½ mark
$A B + B C = 5 + 5 = 25 = A C$ , so A, B, C are collinear.
½ mark

Answer: AB = BC = $5$ , AC = $25$ ; AB + BC = AC, so the points are collinear.

Where the marks are

Finds AB $= 5$ (½ mark)
Finds BC $= 5$ (½ mark)
Finds AC $= 25$ (½ mark)
Shows AB + BC = AC and concludes collinear (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/5/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2025: question 25

Hints

Step-by-step solution

Revise the chapter

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