Question
Let AP and BQ be two vertical poles at points A and B, respectively. If AP = 16 m. BQ = 22 m and AB = 20 m, then find the distance of a point R on AB from the point A such that RP2 + RQ2 is minimum.
Solution
Let R be a point on AB such that AR = x metres, RB = (20 – x) metres
∴ RP2 = AR2 + AP2 = x2 + (16)2 = x2+ 256
and RQ2 = RB2 + BQ2
= (20 – x)2 + (22)2
= 400+ x2 – 40 x + 484
= x2 – 40 x + 884
Let y = RP2 + RQ2
