How many lattice points are enclosed by the triangle with vertices (0,99),(5,100), and (2003,500)? Don't count boundary points.
A number or a short expression. Spacing and $ signs are ignored.
Solution
Using the determinant formula, we get that the area of the triangle is 520031401/2=1 There are 4 lattice points on the boundary of the triangle (the three vertices and (1004,300) ), so it follows from Pick's Theorem that there are 0 in the interior.
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