MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 25

From the official CBSE sample question paper for 2024-25, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerCoordinate Geometry

Show that the points $A (- 5, 6)$ , $B (3, 0)$ and $C (9, 8)$ are the vertices of an isosceles triangle.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

An isosceles triangle has two equal sides.

Hint 2

Find all three side lengths with the distance formula and compare them.

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.

$A B = (3 + 5)^{2} + (0 - 6)^{2} = 64 + 36 = 100 = 10$ units
½ mark
$B C = (9 - 3)^{2} + (8 - 0)^{2} = 36 + 64 = 100 = 10$ units
½ mark
$A C = (9 + 5)^{2} + (8 - 6)^{2} = 196 + 4 = 200 = 102$ units
½ mark
$A B + B C = 20 > 102 = A C$ , so the points are not collinear and form a triangle. Since $A B = B C = 10$ units, $△ A B C$ is isosceles.
½ mark

Answer: $A B = B C = 10$ , $A C = 102$ , so $△ A B C$ is isosceles.

Where the marks are

Finds $A B = 10$ (½ mark)
Finds $B C = 10$ (½ mark)
Finds $A C = 102$ (½ mark)
Concludes the triangle is isosceles because two sides are equal (½ 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 paperSample paper 2024-25 (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 sample paper 2024-25: question 25

Hints

Step-by-step solution

Revise the chapter

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