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

CBSE Class 10 Mathematics Basic 2025: question 23

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCoordinate Geometry

Find the coordinates of the points of trisection of line segment joining the points $(- 4, 1)$ and $(6, 5)$ .

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

Points of trisection divide the segment into three equal parts. In what ratios do they divide it?

Hint 2

Apply the section formula $(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$ with ratios 1 : 2 and 2 : 1.

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(−4, 1), B(6, 5) and let P, Q be the points of trisection so that AP = PQ = QB. Then P divides AB in the ratio 1 : 2.
By section formula, $P = (\frac{1 ( 6 ) + 2 ( - 4 )}{3}, \frac{1 ( 5 ) + 2 ( 1 )}{3}) = (\frac{- 2}{3}, \frac{7}{3})$
1 mark
Q divides AB in the ratio 2 : 1.
$Q = (\frac{2 ( 6 ) + 1 ( - 4 )}{3}, \frac{2 ( 5 ) + 1 ( 1 )}{3}) = (\frac{8}{3}, \frac{11}{3})$
1 mark

Answer: $(- \frac{2}{3}, \frac{7}{3})$ and $(\frac{8}{3}, \frac{11}{3})$

Where the marks are

Uses ratio 1 : 2 and finds P $(- \frac{2}{3}, \frac{7}{3})$ (1 mark)
Uses ratio 2 : 1 and finds Q $(\frac{8}{3}, \frac{11}{3})$ (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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 23

Hints

Step-by-step solution

Revise the chapter

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