MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 27

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerCoordinate Geometry

Find the coordinates of the points of trisection of the line segment joining the points A(−1, 4) and B(−3, −2).

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Points of trisection divide AB in ratios 1 : 2 and 2 : 1.

Hint 2

Use $(\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}})$ with A(−1, 4), B(−3, −2).

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 P and Q be the points of trisection, so A, P, Q, B in order with AP : PB = 1 : 2. By the section formula, $P = (\frac{1 ( - 3 ) + 2 ( - 1 )}{1 + 2}, \frac{1 ( - 2 ) + 2 ( 4 )}{1 + 2})$
1 mark
$P = (\frac{- 5}{3}, \frac{6}{3}) = (- \frac{5}{3}, 2)$
½ mark
Q is the mid-point of PB: $Q = (\frac{- \frac{5}{3} + ( - 3 )}{2}, \frac{2 + ( - 2 )}{2})$
1 mark
$Q = (\frac{- 14/3}{2}, 0) = (- \frac{7}{3}, 0)$
½ mark

Answer: $(- \frac{5}{3}, 2)$ and $(- \frac{7}{3}, 0)$

Where the marks are

Applies section formula for ratio 1 : 2 (1 mark)
Gets $P (- \frac{5}{3}, 2)$ (½ mark)
Uses mid-point of PB or ratio 2 : 1 for Q (1 mark)
Gets $Q (- \frac{7}{3}, 0)$ (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 30/2/1 (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 27

Hints

Step-by-step solution

Revise the chapter

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