MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 29(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, 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

Prove that the point P dividing the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 3 : 2, lies on the line $x - 3 y = - 1$ . Also find length of PA and PB.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Use the section formula $(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ .

Hint 2

A point lies on a line if its coordinates satisfy the equation.

Hint 3

Use the distance formula for PA and PB.

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.

By the section formula with $m : n = 3 : 2$ , A(–1, 7), B(4, –3):
$P = (\frac{3 ( 4 ) + 2 ( - 1 )}{5}, \frac{3 ( - 3 ) + 2 ( 7 )}{5}) = (\frac{10}{5}, \frac{5}{5}) = (2, 1)$
1 mark
Put $x = 2, y = 1$ in $x - 3 y$ : $2 - 3 (1) = - 1 =$ RHS. So P lies on the line $x - 3 y = - 1$ .
1 mark
$P A = (2 + 1)^{2} + (1 - 7)^{2} = 9 + 36 = 45 = 35$ units
½ mark
$P B = (2 - 4)^{2} + (1 + 3)^{2} = 4 + 16 = 20 = 25$ units
½ mark

Answer: P(2, 1) lies on $x - 3 y = - 1$ ; PA $= 35$ units, PB $= 25$ units

Where the marks are

Finds P = (2, 1) by section formula (1 mark)
Verifies P satisfies $x - 3 y = - 1$ (1 mark)
PA $= 35$ (½ mark)
PB $= 25$ (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Finding the Ratio and Unknowns with Section 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 paper2026 board paper, set 30/5/1 (Standard): 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 Standard 2026: question 29(b)

Hints

Step-by-step solution

Revise the chapter

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