MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 22

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, 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

The coordinates of the end points of the line segment AB are A $(- 2, - 2)$ and B $(2, - 4)$ . P is the point on AB such that $B P = \frac{4}{7} A B$ . Find the coordinates of point P.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

If BP is $\frac{4}{7}$ of AB, what fraction of AB is AP?

Hint 2

Use the ratio $A P : P B$ in the section formula $(\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}})$ .

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.

$B P = \frac{4}{7} A B$ , so $A P = \frac{3}{7} A B$ . Hence P divides AB internally in the ratio $A P : P B = 3 : 4$ .
½ mark
By the section formula with $m_{1} = 3$ , $m_{2} = 4$ , A $(- 2, - 2)$ and B $(2, - 4)$ : $x = \frac{3 ( 2 ) + 4 ( - 2 )}{3 + 4} = \frac{- 2}{7}$
½ mark
$y = \frac{3 ( - 4 ) + 4 ( - 2 )}{3 + 4} = \frac{- 20}{7}$
½ mark
Hence the coordinates of P are $(- \frac{2}{7}, - \frac{20}{7})$ .
½ mark

Answer: $P (- \frac{2}{7}, - \frac{20}{7})$

Where the marks are

Finds the ratio $A P : P B = 3 : 4$ (½ mark)
Finds the x-coordinate $- \frac{2}{7}$ (½ mark)
Finds the y-coordinate $- \frac{20}{7}$ (½ mark)
States P correctly (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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 22

Hints

Step-by-step solution

Revise the chapter

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