April 10th, 2011, 03:15 PM  #1 
Newbie Joined: Mar 2011 Posts: 8 Thanks: 0  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! 
April 10th, 2011, 03:49 PM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  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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