21 Jan
2004
21 Jan
'04
11:57 a.m.
At 01:20 PM 1/21/04, David Wilson wrote:
Is every rational point on the plane equidistant from two integer points?
Yes. Let the rational point be P = (p/q, r/s). Arbitrarily suppose that the midpoint of the integer points is the origin. The line from the origin to P is the perpendicular bisector of the line segment between the integer points, so the slope of the latter must be -ps/qr. Thus the integer points can be (qr,-ps) and (-qr,ps). -- Fred W. Helenius <fredh@ix.netcom.com>