Question

With out Pythagoras theorem, show that A(4, 4), B(3, 5) and C(-1, -1) are the vertices of a right angled.

Answer 1

Slope of BC = m₁ = `(-1 - 5)/(-1 - 3) = (3)/(2)`
Slope of CA = m₂ = `(4 - (-1))/(4 - (-1)` = 1
Also, slope of AB = m₃ - `(5 - 4)/(3 - 4)` = -1
Since, m₂m₃ = 1 x (-1) = -1, So, AB and CA are perpendicular to each.
Thus, ΔABC is a right angled triangle at A.
Hence proved.