MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 31(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section C, question 31(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(b) · 3 marks · Short answerCoordinate Geometry

The line segment joining the points $A (-5, 1)$ and $B (7, 6)$ is trisected at the points P and Q such that P is nearer to A. If P lies on the line $x + y = k$ , then find the value of $k$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Trisection divides AB into three equal parts; in what ratio does P divide AB?

Hint 2

Apply the section formula with ratio $1 : 2$ .

Hint 3

Substitute the coordinates of P into $x + y = k$ .

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.

P is the point of trisection nearer to A, so $A P : P B = 1 : 2$ .
½ mark
By section formula, $P = (\frac{1 \times 7 + 2 \times ( - 5 )}{1 + 2}, \frac{1 \times 6 + 2 \times 1}{1 + 2}) = (\frac{- 3}{3}, \frac{8}{3}) = (- 1, \frac{8}{3})$
1½ marks
P lies on $x + y = k$ : $k = - 1 + \frac{8}{3} = \frac{5}{3}$
1 mark

Answer: $k = \frac{5}{3}$

Where the marks are

Identifies ratio $A P : P B = 1 : 2$ (½ mark)
Finds $P (- 1, \frac{8}{3})$ by section formula (1½ marks)
Substitutes in $x + y = k$ to get $k = \frac{5}{3}$ (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 paper2026 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 2026: question 31(b)

Hints

Step-by-step solution

Revise the chapter

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