MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 29(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section C, question 29(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(b) · 3 marks · Short answerCoordinate Geometry

A(6, $- 3$ ), B(0, 5) and C $(- 2, 1)$ are vertices of $Δ$ ABC. Points P(3, 1) and Q(2, $- 1$ ) lie on sides AB and AC respectively. Check whether $\frac{A P}{P B} = \frac{A Q}{QC}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Use the distance formula $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ for each of the four lengths.

Hint 2

Compute AP, PB, AQ and QC, then form the two ratios and compare them.

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.

$A P = (3 - 6)^{2} + (1 + 3)^{2} = 9 + 16 = 5$
½ mark
$P B = (0 - 3)^{2} + (5 - 1)^{2} = 9 + 16 = 5$
½ mark
$A Q = (2 - 6)^{2} + (- 1 + 3)^{2} = 16 + 4 = 25$
½ mark
$QC = (- 2 - 2)^{2} + (1 + 1)^{2} = 16 + 4 = 25$
½ mark
$\frac{A P}{P B} = \frac{5}{5} = 1$ and $\frac{A Q}{QC} = \frac{2 5}{2 5} = 1$ . Therefore $\frac{A P}{P B} = \frac{A Q}{QC}$ . Yes, the ratios are equal.
1 mark

Answer: Yes, $\frac{A P}{P B} = \frac{A Q}{QC} = 1$

Where the marks are

$A P = 5$ (½ mark)
$P B = 5$ (½ mark)
$A Q = 25$ (½ mark)
$QC = 25$ (½ mark)
Both ratios equal 1, hence equal (1 mark)

Revise the chapter

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

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 430/4/1 (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 29(b)

Hints

Step-by-step solution

Revise the chapter

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