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area of right triangle A(T) = E/2+I -1 - Chile 2002 L2 P5

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September 1, 2022
geometryanalytic geometrychilean NMO

Problem Statement

Given a right triangle TT, where the coordinates of its vertices are integers, let EE be the number of points of integer coordinates that belong to the edge of the triangle TT, II the number of points of integer coordinates that belong to the interior of the triangle TT. Show that the area A(T)A(T) of triangle TT is given by: A(T)=E2+I−1A(T) = \frac{E}{2}+I -1.
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