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Prove that S(ABC) is no larger than 9/2

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September 19, 2010
analytic geometrygeometry

Problem Statement

In coordinate plane, we call a point (x,y)(x, y) "lattice point" if both xx and yy are integers. Knowing that the vertices of triangle ABCABC are all lattice points, and there exists exactly one lattice point interior to triangle ABCABC (there might exist lattice points on the sides of ABCABC). Prove that the area of triangle ABCABC is no larger than 92.\frac 92.
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