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Math Help - Coordinate Question

  1. #1
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    Coordinate Question

    An integer point has integer coordinates. Also call point (x,y) different if all the distances from (x,y) to integer points are different.

    Show that (3/4, 2/5) is not different
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  2. #2
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    Re: Coordinate Question

    So you want to show that there exist points (x_1, y_1) and (x_2, y_2), either x_1\ne x_2 or y_2\ne y_1, such that \sqrt{(x_1- 3/4)^2+ (y_1- 2/5)^2}= \sqrt{(x_2- 3/4)^2+ (y_2- 2/5)^2}.

    I recommend starting by squaring both sides. You can then write the equation in terms of x_1- x_2 and y_1- y_2. Obviously one solution will be x_1= x_2 and y_1= y_2 but there is another solution. Find it.
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