Question 147597
Let the end points with midpoint (3,-1) be (a,b) and (c,d)
Let the end points with midpoint (4,3) be (c,d) and (e,f)
Then the end points with midpoint (0,5) are (e,f) and (a,b)
------------------
Note: Each coordinate of a midpoint is the average of the corresponding 
coordinates of the end points. 
For example (a+c)/2 = 3 and (b+d)/2 = -1
Therefore a+c = 6 and b+d = -1
----------------------
Using that same idea on the three midpoints you get 6 equations with 6 variables:
a + 0 + c + 0 + 0 + 0  = 6
a + 0 + 0 + 0 + e + 0  = 0
0 + 0 + c + 0 + e + 0  = 8
0 + b + 0 + d + 0 + 0  = -2
0 + 0 + 0 + d + 0 + f  = 6
0 + b + 0 + 0 + 0 + f  = 10
------------------------------
Solve that system of equations using any method to get:
a = -1
b = 1
c = 7
d = -3
e = 1
f = 9
============
Cheers,
Stan H.