MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 27(B)

From the official CBSE sample question paper for 2024-25, section C, question 27(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(B) · 3 marks · Short answerCoordinate Geometry

Line $4 x + y = 4$ divides the line segment joining the points $(- 2, - 1)$ and $(3, 5)$ in a certain ratio. Find the ratio.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

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

That point lies on the line, so its coordinates satisfy $4 x + y = 4$ .

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 $4 x + y = 4$ meet the segment joining $A (- 2, - 1)$ and $B (3, 5)$ at $P (x_{1}, y_{1})$ , with $A P : P B = k : 1$ . By the section formula:
$x_{1} = \frac{3 k - 2}{k + 1}$ , $y_{1} = \frac{5 k - 1}{k + 1}$
1 mark
Since P lies on $4 x + y = 4$ :
$4 (\frac{3 k - 2}{k + 1}) + \frac{5 k - 1}{k + 1} = 4$
½ mark
$12 k - 8 + 5 k - 1 = 4 k + 4 \Rightarrow 13 k = 13 \Rightarrow k = 1$
1 mark
Hence the required ratio is $1 : 1$ .
½ mark

Answer: $1 : 1$

Where the marks are

Coordinates of P by the section formula in ratio $k : 1$ (1 mark)
Substitutes P into $4 x + y = 4$ (½ mark)
Solves to get $k = 1$ (1 mark)
States the ratio $1 : 1$ (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 paperSample paper 2024-25 (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 sample paper 2024-25: question 27(B)

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry