AHSME 1993 Problem 28

How many triangles with positive area are there whose vertices are points in the $xy$-plane whose coordinates are integers $(x,y)$ satisfying $1\le x\le 4$ and $1\le y\le 4$? $\text{(A) } 496 \text{(B) } 500 \text{(C) } 512 \text{(D) } 516 \text{(E) } 560$