Question

Hello everyone! Can someone please help me, I don`t understand....

Help would be really appreciated. Thank you.


Is Δ ABC a right-angled triangle? A(3, -3), B(2, 1) and C(7, -2). Show your work and explain how you arrived at your answer

Answer 1

Explanation:

You have to find the slope

Slope= y₂ - y₁ / x₂-x₁

A(3, -3), B(2, 1)

Slope of AB m₁ = 1-[-3] / 2-3 = 1+3 / -1 = 4/-1 = -4

B(2, 1) ; C(7, -2)

slope of BC m₂= -2-1 / 7-2 = -3/5

A(3, -3) ; C(7, -2)

Slope of AC m₃ = -2-[-3] / 7-3 = -2+3 / 4 = 1/4

m₁ * m₃ = -4 * (1/4) = -4/4 = -1

When the product of slope is (-1), then two lines are perpendicular.

So AB and AC are perpendicular. Δ ABC is a right-angled triangle