Pick’s theorem: A = B + I − 1Pick’s theorem is an interesting yet little known formula for...

Pick’s theorem: A = B + I − 1

Pick’s theorem is an interesting yet little known formula for computing the area of a polygon drawn in the Cartesian coordinate system. The formula can be applied as long as the vertices of the polygon are lattice points (both x and y are integers). If B represents the number of lattice points lying directly on the boundary of the polygon (including the vertices), and I represents the number of points in the interior, the area of the polygon is given by the formula shown. Use some graph paper to carefully draw a triangle with vertices at (−3, 1), (3, 9), and (7, 6), then use Pick’s theorem to compute the triangle’s area.