Answer: ABCD is a parallelogram.
Step-by-step explanation:
First we plot these point on a graph as given in attachment.
From the attachment we can observe that AD || BC || x-axis .
also, AB ||CD, that will make ABCD a parallelogram , but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".
Mid point of AC= 
Mid point of BD= 
Thus, Mid point of AC=Mid point of BD
i.e. diagonals bisect each other.
That means ABCD is a parallelogram.
So really all you have to do is simply the expressions on top to match them.
Starting with (4t-8/5)-(3-4/3t), distribute the negative sign to the right portion in parentheses, then distribute it all out and you will get 16/3t- 23/5
Basically, use distribution to simplify, here's all the matches:
(4t-8/5)-(3-4/3t) --> 16/3t- 23/5
5(2t+1)+(-7t+28) --> 3t+33
(-9/2t+3)+(7/4t+33) --> -11/4t+36
3(3t-4)-(2t+10) --> 7t-22
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.
