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

CBSE Class 10 Mathematics Standard 2026: question 30

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

Q30 · 3 marks · Short answerCoordinate Geometry

A point P(x, 7) divides a line segment joining the points A(-5, 4) and B(7, 9) in a certain ratio. Find the ratio and hence find the value of x.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

The y-coordinate of P is known. Use it in the section formula with ratio k : 1.

Hint 2

Once you have the ratio, use the section formula for the x-coordinate.

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 divide AB in the ratio $k : 1$ , that is, $A P : P B = k : 1$ .
½ mark
Using the section formula for the y-coordinate:
$7 = \frac{k \cdot 9 + 1 \cdot 4}{k + 1}$
$\Rightarrow 7 k + 7 = 9 k + 4 \Rightarrow k = \frac{3}{2}$
1 mark
So the ratio is $\frac{3}{2} : 1 = 3 : 2$ .
½ mark
Using the section formula for the x-coordinate with ratio $3 : 2$ :
$x = \frac{3 \times 7 + 2 \times ( - 5 )}{3 + 2} = \frac{21 - 10}{5} = \frac{11}{5}$
1 mark

Answer: Ratio 3 : 2; $x = \frac{11}{5}$

Where the marks are

Takes the ratio as k : 1 (½ mark)
Uses the y-coordinate in the section formula to get k = 3/2 (1 mark)
States the ratio 3 : 2 (½ mark)
Finds x = 11/5 (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 30/3/1 (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 30

Hints

Step-by-step solution

Revise the chapter

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