MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 28

From the official CBSE sample question paper for 2026-27, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCoordinate Geometry

Determine the ratio in which the point $(- 6, y)$ divides the line segment joining the points A $(- 3, - 1)$ and B $(- 8, 9)$ . Also, find the value of $y$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Let the ratio be $k : 1$ and write the coordinates of the dividing point.

Hint 2

Equate the x-coordinate to $- 6$ to find $k$ , then substitute to get $y$ .

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 point $(- 6, y)$ divide AB in the ratio $k : 1$ .
½ mark
By the section formula, the point is $(\frac{- 8 k - 3}{k + 1}, \frac{9 k - 1}{k + 1})$
½ mark
$\frac{- 8 k - 3}{k + 1} = - 6 \Rightarrow - 8 k - 3 = - 6 k - 6 \Rightarrow k = \frac{3}{2}$ , so the ratio is $3 : 2$
1 mark
$y = \frac{9 \cdot \frac{3}{2} - 1}{\frac{3}{2} + 1} = \frac{\frac{25}{2}}{\frac{5}{2}} = 5$
1 mark

Answer: Ratio 3 : 2 (internally); $y = 5$

Where the marks are

Takes the ratio as k : 1 (½ mark)
Writes the section formula coordinates (½ mark)
Finds k = 3/2, i.e. 3 : 2 (1 mark)
Finds y = 5 (1 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 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 28

Hints

Step-by-step solution

Revise the chapter

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