Question

Without using Pythagoras theorem show that points A(4, 4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.

Answer 1

Given, A(4, 4), B(3, 5), C(−1, −1).

Slope of AB = `(y_2 - y_1)/(x_2 - x_1) = (5 - 4)/(3 - 4)` = −1

Slope of BC = `(-1 - 5)/(-1 - 3) = (-6)/(-4) = 3/2`

Slope of AC = `(-1 - 4)/(-1 - 4)` = 1

Slope of AB x slope of AC = −1 × 1 = −1

∴ side AB ⊥ side AC

Thus ΔABC is a right angled triangle right angled at A.

∴ The given points are the vertices of a right angled triangle.