Your diagram is correct.
I would have however written the Given as stated
Given :
XB≅XA≅AY≅YB ( If they are equidistant then they are all the same distance, thus the values will all be equal)
Prove:
<x≅<b≅<y≅<a (this is because a square is formed) < is angle
XM≅YM≅AM≅MB (The fact that the previous statements are true means that this is a square, if M is the midpoint than all these segments are equal)
MX≅MY
Im not sure what you did wrong besides maybe you didn't prove it well enough, everything is correct that you have written. I cant read the pen but it looks like you were missing a step.
