Question

The triangle whose vertices are $(5,7), (2,7)$ and $(5,2)$ is a _____ triangle.

• A. Equilateral
• B. Isosceles
• C. Right angle
• D. Scalene

Hint:

If $a^2 + b^2 = c^2$, the triangle is right-angled.

Answer 1

The Correct Option is C

Concept: Use distance formula to check Pythagoras theorem.
Step 1: Find side lengths.
\[ AB = \sqrt{(5-2)^2 + (7-7)^2} = 3 \] \[ AC = \sqrt{(5-5)^2 + (7-2)^2} = 5 \] \[ BC = \sqrt{(2-5)^2 + (7-2)^2} = \sqrt{9 + 25} = \sqrt{34} \]
Step 2: Check Pythagoras.
\[ 3^2 + 5^2 = 9 + 25 = 34 = (\sqrt{34})^2 \]
Hence, the triangle is right-angled.