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Area Smaller, Smaller...

Source: 1992 National High School Mathematics League, Exam Two, Problem 3

February 27, 2020
geometry

Problem Statement

In coordinate system, there are six points Pi(xi,yi)(i=1,2,⋯ ,6)P_i(x_i,y_i)(i=1,2,\cdots,6), satisfying: (1) xi,yi∈{−2,−1,0,1,2}x_i,y_i\in\{-2,-1,0,1,2\}. (2) For any three points, they are not collinear. Prove that there exists a triangle △PiPjPk(1≤i<j<k≤6)\triangle P_iP_jP_k(1\leq i<j<k\leq6), its area is not larger than 22.
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