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April 10th, 2011, 03:15 PM   #1
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Equidistant points

Hello, here is a cool problem that I can't solve and would like to finally see a unifying proof for...
is it possible for a point Q=(r,s) where r and s are rational, for r and s to be RATIONAL numbers without being equidistant from any two lattice points (lattice point- a point with integer x and y coordinates)?
Thanks!
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April 10th, 2011, 03:49 PM   #2
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Re: Equidistant points

What makes it "cool"? This wouldn't happen to be a homework problem, would it?

Notice that if Q is equidistant from points, say, A and B, then Q is on the perpendicular bisector of (segment) AB. This might help you (dis)prove the statement.
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