It seems to me that you are getting P by rotating A around 0 by +90 degrees, whereas you are getting Q by rotating B around 0 by -90 degrees. Which is right: rotating by +90 or rotating by -90 degrees?
Since M is mid point of QP, then QM = 1/2 (p-q)
=1/2(z1-z2) + i/2 (z1+ z2)
But QM = M - z2
z2 + QM = M
M = 1/2 ((z1+z2) + i(z1 + z2))
However solutions has 1/2(z1+z2 + i(z1-z2))
Thanks in advance.