1993 AHSME 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\quad \text{(B) } 500\quad \text{(C) } 512\quad \text{(D) } 516\quad \text{(E) } 560

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.