MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 28

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCoordinate Geometry

Find the ratio in which the y-axis divides the line segment joining the points $(5, - 6)$ and $(- 1, - 4)$ . Also find the point of intersection.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

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

Hint 1

Every point on the y-axis has x-coordinate 0.

Hint 2

Let the ratio be $k : 1$ and write the x-coordinate of the dividing point using the section formula.

Hint 3

Put that x-coordinate equal to 0 to find $k$ . Then use $k$ in the formula for the y-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 $A (5, - 6)$ and $B (- 1, - 4)$ . Any point on the y-axis has x-coordinate 0, so let the y-axis cut $A B$ at $P (0, y)$ . Let $P$ divide $A B$ in the ratio $k : 1$ .
½ mark
Section formula for the x-coordinate: $x = \frac{k ( - 1 ) + 1 ( 5 )}{k + 1}$ . Since $P$ is on the y-axis, $\frac{- k + 5}{k + 1} = 0$ . So $- k + 5 = 0$ , which gives $k = 5$ .
1 mark
Hence the y-axis divides the segment in the ratio $5 : 1$ (internally).
½ mark
Section formula for the y-coordinate: $y = \frac{5 ( - 4 ) + 1 ( - 6 )}{5 + 1} = \frac{- 20 - 6}{6} = \frac{- 26}{6} = - \frac{13}{3}$ .
½ mark
Point of intersection is $P (0, - \frac{13}{3})$ .
½ mark

Answer: Ratio 5 : 1; point of intersection $(0, - \frac{13}{3})$

Where the marks are

Takes the point as $(0, y)$ and the ratio as $k : 1$ (½ mark)
Sets the x-coordinate from the section formula equal to 0 and gets $k = 5$ (1 mark)
States the ratio as 5 : 1 (½ mark)
Finds $y = - \frac{13}{3}$ (½ mark)
States the point $(0, - \frac{13}{3})$ (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 30/1/1 (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 2025: question 28

Hints

Step-by-step solution

Revise the chapter

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