April 10th, 2011, 02:15 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, 02:49 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. 

Tags 
equidistant, points 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Points  aldar13  Algebra  4  April 10th, 2013 07:50 PM 
Find the point on the line that is equidistant from 2 points  elifast  Algebra  6  September 18th, 2012 06:35 PM 
turning points and nature of turning points  harry buckle  Algebra  7  January 25th, 2012 06:16 PM 
accumulation points or limits points  alice 9  Real Analysis  24  November 13th, 2010 02:27 PM 
Find the point on the line that is equidistant from 2 points  elifast  Applied Math  0  December 31st, 1969 04:00 PM 