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Mathematics — CBSE Class 10 board question

Q1. [1]
The points $(-5, 0)$, $(5, 0)$ and $(0, 4)$ are the vertices of a triangle which is a/an :
  1. A right-angled triangle
  2. B isosceles triangle
  3. C equilateral triangle
  4. D scalene triangle
Previously asked in CBSE board exam
2025 30/2/1 Q6
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

Option B: Isosceles triangle

Let A(–5, 0), B(5, 0), C(0, 4).
$AB = \sqrt{(10)^2+0^2} = 10$
$AC = \sqrt{25+16} = \sqrt{41}$
$BC = \sqrt{25+16} = \sqrt{41}$

Since AC = BC ≠ AB, it is an isosceles triangle.

Source: Chapter 7, Section 7.2 (Distance Formula)

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Explanation

The examiner expects you to apply the distance formula to all three sides and observe that two sides are equal (AC = BC = √41) while the third is different (AB = 10). Equal two sides → isosceles. Also verify it is not equilateral (all sides equal) or right-angled (no Pythagoras triplet holds here: 41 + 41 ≠ 100).

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