Question

If the points A, B and C have the coordinates A(5, 2), B(2, −3) and C(−8, 3), show that the triangle ABC is a right-angled triangle.

Answer 1

Answer:

See below.

Step-by-step explanation:

Triangle ABC will be right-angled if 2 of its sides are perpendicular to each other. When sides are perpendicular the product of their slopes = -1.

Slope  of side AB = (-3-2)/(2-5) = -5/-3 = 5/3

Slope of side BC = (3- -3) / -8-2) = 6/-10 = -3/5

The product of the slopes = 5/3 * -3/5 = -15/15 = -1.

So AB is perpendicular to BC  and triangle ABC is right-angled .