Question

In ΔABC, m∠B = 90°, A(2, 3), B(4, 5) and C(a, 2). Then find a.

Answer 1

ΔABC is a right angled Δ

AB2 + BC2 = AC2 ........(i)

AB2 = (4 – 2)2 + (5 – 3)2

⇒4 + 4 = 8

BC2 = (a – 4)2 + (2 – 5)2 = a2 + 16 – 8a + 9

AC2 = (a – 2)2 + (2 – 3)2 = a2 + 4 – 4a + 1

Putting values in equation (i)

8 + a2 + 16 – 8a + 9 = a2 + 4 – 4a + 1

28 = 4a

a = 7.