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    Betweenness and Elementary Figures : Three Collinear Points

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    Let A = (x1,y1), B = (x2,y2), and C = (x,y) be three collinear points in the Euclidean Plane with x1<x2. Prove that A-C-B iff x1<x<x2.

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    Solution Preview

    If C is between A and B, then AC+CB=AB. So (AC+CB)^2=AB^2, we have
    This implies ...

    Solution Summary

    A proof involving collinear points is provided and the details are provided.