Well, it is an algebraic solution to note the following, when traveling from B to A:
Go 3 units to the right (add 3 to x)
Go 5 units down (subtract 5 from y)
So from that, one can write
j = Cx + 3
k = Cy - 5
Therefore, j = 2+3 = 5 and k = 4-5 = -1
Thus, D is at (5,-1).
One way to check this is to make sure the two diagonals are equal length:
A-C: 
B-D: 
so the two diagonals are equal length and the polygon is a square.
