Given that the line segment joining the points A(a, b) and B(c, d) subtends a right angle at the origin O(0, 0)
So, AOB is a right angled triangle with right angle at O.
We got OA2 + OB2 = AB2 [By Pythagoras Theorem]
We know that the distance between the points (x1, y1) and (x2, y2) is
⇒ OA2 + OB2 = AB2
⇒ (0 - a)2 + (0 - b)2 + (0 - c)2 + (0 - d)2 = (a - c)2 + (b - d)2
⇒ a2 + b2 + c2 + d2 = a2 + c2 - 2ac + b2 + d2 - 2bd
⇒ 2ac + 2bd = 0
⇒ ac + bd = 0
