MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 23

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCoordinate Geometry

A $(-2, 3)$ and B $(4, 1)$ are end points of the diameter of a semi-circle. The semi-circle intersects y-axis at point P. Find the co-ordinates of the point P.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

The centre of the circle is the mid-point of the diameter.

Hint 2

A point on the y-axis has x-coordinate 0; write P as $(0, y)$ .

Hint 3

P is on the circle, so its distance from the centre equals the radius.

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.

Centre O is the mid-point of diameter AB: $O = (\frac{- 2 + 4}{2}, \frac{3 + 1}{2}) = (1, 2)$ .
½ mark
Let $P = (0, y)$ (it lies on the y-axis). Since P is on the circle, $O P = O B$ (radii): $O P^{2} = O B^{2} \Rightarrow (0 - 1)^{2} + (y - 2)^{2} = (4 - 1)^{2} + (1 - 2)^{2}$
$1 + (y - 2)^{2} = 10 \Rightarrow (y - 2)^{2} = 9 \Rightarrow y - 2 = \pm 3 \Rightarrow y = 5$ or $y = - 1$
1 mark
Hence P is $(0, 5)$ or $(0, - 1)$ (depending on which side of AB the semi-circle lies; the figure shows it above AB, giving $(0, 5)$ ).
½ mark

Answer: P(0, 5) or P(0, −1)

Where the marks are

Finds centre $(1, 2)$ using mid-point formula (½ mark)
Sets $O P^{2} = O B^{2}$ and solves to get $y = 5$ or $- 1$ (1 mark)
States coordinates of P (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Midpoint Formula and Points of Trisection

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 430/4/1 (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 2026: question 23

Hints

Step-by-step solution

Revise the chapter

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