MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 27

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerCoordinate Geometry

Find the ratio in which the $x$ -axis divides the line segment joining the points $(- 6, 5)$ and $(- 4, - 1)$ . Also, find the point of intersection.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

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

Let the ratio be k : 1 and write the coordinates of the dividing point by the section formula.

Hint 3

Make the y-coordinate zero to find k, then substitute k back to get 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 A(−6, 5) and B(−4, −1). Let the x-axis meet AB at P(x, 0), and let P divide AB in the ratio $k : 1$ .
½ mark
By the section formula,
$P = (\frac{k ( - 4 ) + 1 ( - 6 )}{k + 1}, \frac{k ( - 1 ) + 1 ( 5 )}{k + 1}) = (\frac{- 4 k - 6}{k + 1}, \frac{- k + 5}{k + 1})$
1 mark
P lies on the x-axis, so its y-coordinate is 0:
$\frac{- k + 5}{k + 1} = 0 \Rightarrow k = 5$
½ mark
Hence the x-axis divides the segment in the ratio $5 : 1$ .
½ mark
x-coordinate of P $= \frac{- 4 ( 5 ) - 6}{5 + 1} = \frac{- 26}{6} = - \frac{13}{3}$ .
So the point of intersection is $(- \frac{13}{3}, 0)$ .
½ mark

Answer: Ratio 5 : 1; point of intersection $(- \frac{13}{3}, 0)$

Where the marks are

Takes P(x, 0) dividing AB in ratio k : 1 (½ mark)
Writes the coordinates of P by the section formula correctly (1 mark)
Sets the y-coordinate to 0 and gets k = 5 (½ mark)
States the ratio 5 : 1 (½ mark)
Finds the point $(- \frac{13}{3}, 0)$ (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 paper2026 board paper, set 30/1/1 (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 2026: question 27

Hints

Step-by-step solution

Revise the chapter

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