Question

Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.

Answer 1

$\text{Slope of}AB=\frac{y_2-y_1}{x_2-x_1}=\frac{2-4}{1-0}=-2\text{Slope of}BC=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{3-1}=\frac{1}{2}\text{Slope of}AB\times \text{Slope of}BC=-2\times \frac{1}{2}=-1\therefore \text{Angle between AB and}BC=\frac{\pi }{2}\therefore \text{ABC are the vertices of a right angled triangle.}$