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existence of points inside polygon with integral differences

Source: Croatia MO 2001 2nd Grade P4

April 22, 2021
geometry

Problem Statement

On the coordinate plane is given a polygon P\mathcal P with area greater than 11. Prove that there exist two different points (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) inside the polygon P\mathcal P such that x1−x2x_1-x_2 and y1−y2y_1-y_2 are both integers.
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