MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 22(a)

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerCoordinate Geometry

Find the ratio in which the point (3, y) divides the line segment joining the points (–2, –5) and (6, 3). Also, find the value of y.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

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

The x-coordinate of the point is known (3); use it to find $k$ first, then put $k$ into 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 $P (3, y)$ divide the join of $(- 2, - 5)$ and $(6, 3)$ in the ratio $k : 1$ . By the section formula:
$3 = \frac{6 k + 1 ( - 2 )}{k + 1}$ , $y = \frac{3 k + 1 ( - 5 )}{k + 1}$
1 mark
$3 k + 3 = 6 k - 2 \Rightarrow 3 k = 5 \Rightarrow k = \frac{5}{3}$ , so the ratio is $\frac{5}{3} : 1 = 5 : 3$ .
½ mark
$y = \frac{3 \cdot \frac{5}{3} - 5}{\frac{5}{3} + 1} = \frac{0}{\frac{8}{3}} = 0$
½ mark

Answer: Ratio 5 : 3; y = 0

Where the marks are

Applies section formula with ratio $k : 1$ for both coordinates (1 mark)
Finds $k = \frac{5}{3}$ , i.e. ratio 5 : 3 (½ mark)
Finds $y = 0$ (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 430/5/1 (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 2024: question 22(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry