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

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 30

From the official CBSE sample question paper for 2026-27, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerCoordinate Geometry

In what ratio does the x-axis divide the line segment joining the points $(- 4, - 6)$ and $(- 1, 7)$ ? Also, find the coordinates of the point of division.

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

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

Hint 2

Take the ratio as $k : 1$ , write the y-coordinate of the dividing point by the section formula, set it equal to 0 and solve for $k$ . Then find the x-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 the x-axis divide the segment joining $A (- 4, - 6)$ and $B (- 1, 7)$ at $P (x, 0)$ in the ratio $k : 1$ .
By the section formula:
$P = (\frac{k ( - 1 ) + 1 ( - 4 )}{k + 1}, \frac{k ( 7 ) + 1 ( - 6 )}{k + 1}) = (\frac{- k - 4}{k + 1}, \frac{7 k - 6}{k + 1})$ .
1 mark
P lies on the x-axis, so its y-coordinate is 0:
$\frac{7 k - 6}{k + 1} = 0 \Rightarrow k = \frac{6}{7}$ .
½ mark
So the x-axis divides the segment in the ratio $6 : 7$ .
½ mark
x-coordinate of P:
$x = \frac{- \frac{6}{7} - 4}{\frac{6}{7} + 1} = \frac{- \frac{34}{7}}{\frac{13}{7}} = - \frac{34}{13}$ .
Point of division is $(- \frac{34}{13}, 0)$ .
1 mark

Answer: Ratio 6 : 7; point of division $(- \frac{34}{13}, 0)$

Where the marks are

Writes the coordinates of P using the section formula with ratio $k : 1$ (1 mark)
Puts y-coordinate = 0 and gets $k = \frac{6}{7}$ (½ mark)
States the ratio 6 : 7 (½ mark)
Finds the point $(- \frac{34}{13}, 0)$ (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 (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 sample paper 2026-27: question 30

Hints

Step-by-step solution

Revise the chapter

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