Question

Let A(3, 4) and B(7, 13) are two fixed points. If 'P' be a point of the line y = x such that PA + PB is minimum, then coordinates of 'P' is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let ${}^{\prime }{A}_1^{\prime }$ is the reflection of A in y = x

${\Rightarrow }^{\prime }{A}_1^{\prime }$ = (4, 3). Now, PA + PB = ${}^{\prime }{A}_1^{\prime }$ P + PB, which is minimum, if ${}^{\prime }{A}_1^{\prime }$ , P and B are collinear. Equation of $A_{1}B$ is
$(y-3)=\frac{13-3}{7-4}(x-4)$
3y = 10x – 31
Solving it with y = x, we get
$P=(\frac{31}{7},\frac{31}{7})$
Hence, (c) is the correct answer.