A simple fact, but hard to derive...

In the (x,y) plane, Point P, at (3,8) is reflected across line m to create point P', and then across line n to create point P". Lines m and n both have a slope of 3/4, and they are 5 units apart.

Find the sum of all x and y coordinates of all possible final positions of P".

For instance, if there are three possible positions that P" could be at, (a,b) , (c,d) and (e,f), your answer would be a+b+c+d+e+f.