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189 geometry/lattice/area.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

189 geometry/lattice/area.p


Prove that the area of a triangle formed by three lattice points is integer/2.

geometry/lattice/area.s

The formula for the area is

A = | x1*y2 + x2*y3 + x3*y1 - x1*y3 - x2*y1 - x3*y2 | / 2

If the xi and yi are integers, A is of the form (integer/2)

 

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