Explanation:

Use n instead of 100. Add in the point (n,0) to make a square. Strictly inside the square are (n−2)² lattice points. On the diagonal are n−2 lattice points making (n−2)²−(n−2)=(n−2)(n−3) lattice points inside the total of the two triangles. We want half of these, so we have (n−2)(n−3)² lattice points. Now using 100, (99×98)/2 = 4851