Alternatively,View attachment 34583I'm not sure where to start or how to use coordinate geometry to prove that AMD is isosceles.
Now you have those facts you could use Pythagoras' Theorem to deduce something (equally important) about MA & MD, hence....If M is the midpoint of BC, then what do you know about the lengths of BM and MC?
Since ABCD is a rectangle, what do you know about the lengths of BA and CD?