Question 1191706
<pre>

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:   {{{ sqrt((2-0)^2 + (4-(-4))^2) = sqrt(2^2 + 8^2) = sqrt(4+64) = sqrt(68) }}}
  B-D:   {{{ sqrt((5-(-3))^2 + (-1-1)^2) = sqrt(8^2+(-2)^2) = sqrt(64+4) = sqrt(68) }}}   so the two diagonals are equal length and the polygon is a square.