Question 1203060
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Hint:


Label the four points as A,B,C,D


A = (-2,2)
B = (3,4)
C = (5,-1)
D = (0,-3)


This is what the diagram looks like
*[illustration Screenshot_226.png]
I used GeoGebra to make the diagram. 


The goal is to find the location of point E.


One very useful property about squares is the diagonals bisect each other.
Bisect means "to cut in half".
Therefore, AE = EC and BE = ED.
The diagonals intersect to form the center.
This tells us that E is the midpoint of diagonal AC.


To go from A to C, we follow the pathway "down 3, right 7". Cut each of those values in half so we know how to go from A to E.
I'll let the student do this part.


Other methods are possible. One alternative is to find the equations of lines AC and BD. 
Then use substitution or elimination to find the coordinates of point E.
The first method I mentioned is a faster route in my opinion.
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