MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 22

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerCoordinate Geometry

Find the type of triangle $A B C$ formed whose vertices are $A (1, 0)$ , $B (- 5, 0)$ and $C (- 2, 5)$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Use the distance formula to find all three sides.

Hint 2

Compare the side lengths: are any two equal?

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.

$A B = (- 5 - 1)^{2} + (0 - 0)^{2} = 36 = 6$ units
½ mark
$B C = (- 2 + 5)^{2} + (5 - 0)^{2} = 9 + 25 = 34$ units
½ mark
$C A = (1 + 2)^{2} + (0 - 5)^{2} = 9 + 25 = 34$ units
½ mark
Since $B C = C A = 34$ , two sides are equal. Also $34 + 34 \neq = 36$ , so it is not right-angled. Hence $△ A B C$ is an isosceles triangle.
½ mark

Answer: Isosceles triangle ( $B C = C A = 34$ , $A B = 6$ )

Where the marks are

$A B = 6$ (½ mark)
$B C = 34$ (½ mark)
$C A = 34$ (½ mark)
Concludes isosceles since $B C = C A$ (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 paper2024 board paper, set 30/2/1 (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 2024: question 22

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry