geometry

prove the following statements using a coordinate proof.

the diagonals of a rectangle bisect each other.

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  1. Choose a rectangle with arbitrary side lengths a and b. The proof will be easier if you locate one corner at the origin (0,0). Let a be the length of the side on the x axis

    Derive equations for the two diagonals.
    One equation will be y1 = (b/a)x
    The other will be y2 = b -(b/a)x

    Set the two equations equal to get the intersection point
    y1 = y2 where (b/a)x = -(b/a)x + b
    2(b/a) x = b
    x = a/2
    y = b/2
    That's clearly the midpoint of the diagonals

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