MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 23

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, 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

If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

The right angle is at B, so AC is the hypotenuse.

Hint 2

Write $A B^{2}$ , $B C^{2}$ and $A C^{2}$ using the distance formula and apply Pythagoras theorem.

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.

Since $∠ B = 9 0^{\circ}$ , by Pythagoras theorem $A C^{2} = A B^{2} + B C^{2}$ .
Using distance formula: $A B^{2} = (a - 1)^{2} + 1$ , $B C^{2} = 1 + (b - 1)^{2}$ , $A C^{2} = a^{2} + b^{2}$
$\Rightarrow a^{2} + b^{2} = (a - 1)^{2} + 1 + 1 + (b - 1)^{2}$
1 mark
$a^{2} + b^{2} = a^{2} - 2 a + b^{2} - 2 b + 4 \Rightarrow 2 a + 2 b = 4 \Rightarrow a + b = 2$
1 mark

Answer: $a + b = 2$

Where the marks are

Uses $A C^{2} = A B^{2} + B C^{2}$ with distance formula correctly (1 mark)
Simplifies to $a + b = 2$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

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 430/5/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 23

Hints

Step-by-step solution

Revise the chapter

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