Answer:
(-14, 5.5)
Explanation:
Perhaps the easiest way to find the 1/4 point is to find (x, y), then find the midpoint between that and M.
(x, y) = 2M -(13, 25) = 2(-5, 12) -(13, 25) = (-23, -1)
Then the 1/4 point is ...
((-23, -1) +M)/2 = ((-23, -1) +(-5, 12))/2 = (-28, 11)/2 = (-14, 5.5)
_____
If we call the end points A(x, y) and B(13, 25), then we know ...
M = (A+B)/2
A = 2M -B . . . . we'll need this in a bit
and the 1/4 point Q is such that ...
(Q -A)/(B -A) = 1/4
4Q -4A = B -A . . . . cross multipliy
Q = (B +3A)/4 = (B +3(2M -B))/4 = (6M -2B)/4 . . . . solve for Q
Q = (3M -B)/2 . . . . reduce the fractions
Q = (3(-5, 12) -(13, 25))/2 = (-28, 11)/2 = (-14, 5.5) . . . as above