coordinate geometry proof (rectangle)

[jj_mathal]

I'm not sure where to start or how to use coordinate geometry to prove that AMD is isosceles.

 

[stapel]

I see no reason to transfer this drawing to the coordinate plane. Just use geometry.

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?

What do you know about the measures of the angles at B and C?

What then can you say about the lengths of AM and DM?

So what sort of triangle must AMD be?

 

[The Highlander]

View attachment 34583I'm not sure where to start or how to use coordinate geometry to prove that AMD is isosceles.

Alternatively,
given the start provided by @stapel,

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?

Now you have those facts you could use Pythagoras' Theorem to deduce something (equally important) about MA & MD, hence....