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Consider the point A= (3, 4), B(7, 13). ...

Consider the point `A= (3, 4), B(7, 13)`. If 'P' be a point on the line `y = x` such that `PA +PB` is minimum then coordinates of P is (A) `(13/7,13,7)` (B) `(23/7,23/7)` (C) `(31/7,31/7)` (D) `(33/7,33/7)`

A

(12/7,12/7)

B

(-24/5,17/5)

C

(31/7,31/7)

D

(0,0)

Text Solution

Verified by Experts

The correct Answer is:
C

Consider a point A', the image of A in y=x. Therefore, the coordinates of A' are (4,3).
Notice that A and B lie on the same side with respect to y=x. Then PA=PA' . Thus, PA+PB is minimum. If PA'+PB is minimum, i.e., if P, A', B are collinear. Now, the equation of A'B is
`y-3 = (13-3)/(7-4)(x-4)`
or 3y-10x+31=0
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