MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 25(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section B, question 25(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(a) · 2 marks · Very short answerCoordinate Geometry

In what ratio is the line segment joining the points $(3, - 5)$ and $(- 1, 6)$ divided by the line $y = x$ ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Take the ratio as $k : 1$ and write the coordinates of the dividing point.

Hint 2

On the line $y = x$ , the two coordinates of a point are equal.

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 the line $y = x$ divide the join of $A (3, - 5)$ and $B (- 1, 6)$ at $P$ in the ratio $k : 1$ . By the section formula, $P = (\frac{- k + 3}{k + 1}, \frac{6 k - 5}{k + 1})$ .
1 mark
$P$ lies on $y = x$ : $\frac{- k + 3}{k + 1} = \frac{6 k - 5}{k + 1} \Rightarrow - k + 3 = 6 k - 5 \Rightarrow 7 k = 8 \Rightarrow k = \frac{8}{7}$ .
½ mark
Required ratio $= \frac{8}{7} : 1 = 8 : 7$ (internally).
½ mark

Answer: 8 : 7

Where the marks are

Coordinates of dividing point by section formula (1 mark)
Uses x-coordinate = y-coordinate to get $k = 8/7$ (½ mark)
Ratio 8 : 7 (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 paper2024 board paper, set 30/2/1 (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 2024: question 25(a)

Hints

Step-by-step solution

Revise the chapter

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