Question

Prove that the points (2, – 2), (- 2, 1) and (5, 2) are the vertices of a right angled triangle. Also, find the area of this triangle.

Answer 1

Let the points A (2, -2), B (-2, 1) and C (5, 2) are the vertices of right angled triangle.

AB² = (- 2 – 2)² + (1 + 2)²

= 16 + 9 = 25

BC² = (5 + 2)² + (2 – 1)² = 49 + 1 = 50

And AC² = (5 – 2)² + (2 + 2)² = 9 + 16 = 25

AB² + AC² = 25 + 25 = 50 = BC²

Since, BC² = AB² + AC²,

So by converse of phythagores theorem ∠A = 90° there fore point A (2, – 2), B (- 2,1) and C (5, 2) are the vertices of a right angled triangle

Here, x₁ = 2, y₁ = -2, x₂ = -2 , y₂ = 1, x₃ = 5, y₃ = 2

Area of ∆ABC