Question

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

Answer 1

Answer:

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 × (- 1) = - 1, So, AB and CA are perpendicular to each other

Thus, ΔABC is a right angled triangle at A.

Hence proved.