Three Colors on a Plane

Date: 03/04/2003 at 20:20:36
From: Scholtes
Subject: Planes and lines

You have three colors, green, red, and blue. These three colors must 
be painted onto a plane. The entire plane is to be covered. When the 
three colors are placed on the plane every straight line that can be 
drawn will pass through exactly two colors. 

How would I draw these colors onto the plane?

Date: 03/06/2003 at 08:35:14
From: Doctor Jacques
Subject: Re: Planes and lines

Hi Scholtes,

Draw a pair of intersecting straight lines, and call O their 
intersection point. Label the 4 regions clockwise as 1, 2, 3, 4.

Now,

* Paint O in red (that will be the only red point)
* Paint regions 1 and 3 in green, and regions 2 and 4 in blue.
* Paint the axes themselves (except for O) in green.

Is this an acceptable solution?

- Doctor Jacques, The Math Forum
  http://mathforum.org/dr.math/