AHSME 1995 Problem 21

Two nonadjacent vertices of a rectangle are $(4,3)$ and $(-4,-3)$, and the coordinates of the other two vertices are integers. The number of such rectangles is $\mathrm{(A) \ 1 } \mathrm{(B) \ 2 } \mathrm{(C) \ 3 } \mathrm{(D) \ 4 } \mathrm{(E) \ 5 }$