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

Consider the point A(3,4) and B(7,13).If P be a point on the line y=x, the co-ordinate of point P if PA+PB is minimum.

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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