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

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

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

Q27(A) · 3 marks · Short answerCoordinate Geometry

Find the ratio in which the y-axis divides the line segment joining the points $(4, - 5)$ and $(- 1, 2)$ . Also find the point of intersection.

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

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

Hint 2

Take the ratio as $k : 1$ and put the x-coordinate from the section formula equal to 0.

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 y-axis meet the segment joining $A (4, - 5)$ and $B (- 1, 2)$ at $P (0, y)$ . Let $A P : P B = k : 1$ .
½ mark
By the section formula, the x-coordinate of P is $\frac{k ( - 1 ) + 1 ( 4 )}{k + 1} = 0$ .
1 mark
$- k + 4 = 0 \Rightarrow k = 4$ . So the required ratio is $4 : 1$ .
½ mark
$y = \frac{4 ( 2 ) + 1 ( - 5 )}{4 + 1} = \frac{8 - 5}{5} = \frac{3}{5}$
½ mark
Hence the point of intersection is $(0, \frac{3}{5})$ .
½ mark

Answer: Ratio $4 : 1$ ; point $(0, \frac{3}{5})$

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 (1 mark)
$k = 4$ , ratio $4 : 1$ (½ mark)
$y = \frac{3}{5}$ (½ mark)
Point $(0, \frac{3}{5})$ (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.

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

Hints

Step-by-step solution

Revise the chapter

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