MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerCoordinate Geometry

Point P $(x, 0)$ divides the line segment joining the points $(2, 8)$ and $(- 3, - 5)$ 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 2025 board paper, set 430/4/1.

Hints

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

Hint 1

Take the ratio as $k : 1$ and use the section formula.

Hint 2

P lies on the x-axis, so its y-coordinate is 0. Use that to find $k$ first.

Hint 3

Once you have the ratio, substitute it into the x-part of the section formula.

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 $(x, 0)$ divide the join of A $(2, 8)$ and B $(- 3, - 5)$ in the ratio $k : 1$ . By the section formula, the $y$ -coordinate of P is $\frac{k ( - 5 ) + 1 ( 8 )}{k + 1} = 0$ .
$- 5 k + 8 = 0 \Rightarrow k = \frac{8}{5}$ . So the required ratio is $8 : 5$ .
1½ marks
$x = \frac{8 ( - 3 ) + 5 ( 2 )}{8 + 5} = \frac{- 24 + 10}{13} = - \frac{14}{13}$
½ mark

Answer: Ratio $8 : 5$ ; $x = - \frac{14}{13}$

Where the marks are

Uses the section formula on the $y$ -coordinate and gets the ratio $8 : 5$ (1½ marks)
Finds $x = - \frac{14}{13}$ (½ 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 430/4/1 (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 2025: question 22

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry