MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 24(b)

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerCoordinate Geometry

Show that the points A(3, 0), B(6, 4) and C(-1, 3) are vertices of a right-angled triangle.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Use the distance formula to find the squares of all three sides.

Hint 2

Check whether the largest square equals the sum of the other two (converse of Pythagoras).

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.

$A B^{2} = (6 - 3)^{2} + (4 - 0)^{2} = 9 + 16 = 25$
½ mark
$B C^{2} = (- 1 - 6)^{2} + (3 - 4)^{2} = 49 + 1 = 50$
½ mark
$A C^{2} = (- 1 - 3)^{2} + (3 - 0)^{2} = 16 + 9 = 25$
½ mark
$A B^{2} + A C^{2} = 25 + 25 = 50 = B C^{2}$ , so by the converse of Pythagoras theorem $△ A B C$ is right-angled at A.
½ mark

Answer: $B C^{2} = A B^{2} + A C^{2}$ , so ABC is right-angled at A.

Where the marks are

$A B^{2} = 25$ (½ mark)
$B C^{2} = 50$ (½ mark)
$A C^{2} = 25$ (½ mark)
Shows $B C^{2} = A B^{2} + A C^{2}$ and concludes right angle (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 430/5/1 (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 2023: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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