$A(4,2)$ and $B(2,4)$ are 2 given points and the point P on the line $3x+2y+10=0$. Find $P$ for which $PA+PB$ is maximum

Question

$A(4,2)$ and $B(2,4)$ are 2 given points and the point P on the line $3x+2y+10=0$ is given then which of the following is or are true:
(a) $(PA+PB)$ is minimum when $P(-14/5,-4/5)$
(b) $(PA+PB)$ is maximum when $P(-14/5,-4/5)$
(c) $|PA-PB|$ is minimum when $P(-22,28)$
(d) $(PA-PB)$ is maximum when $P(-22,28)$

The only way I can think of solving this question is by first figuring out $y=PA+PB$ and then finding the point P when $dy/dx=0$. Then by substituting any other value of $P$ I identify whether the point I figure out was the maxima or the minima. Then I repeat the whole procedure for $y=PA-PB$.

But this seems to be a horribly wrong procedure and I am searching for a shorter method to solve this question. It would be great if someone could help.

Answer 1

I think this diagram should help you.