The question is written like this:

> Is it possible to find an infinite set of points in the plane, not all on the same straight line, such that the distance between **EVERY** pair of points is rational?

This would be so easy if these points could be on the same straight line, but I couldn't get any idea to solve the question above(not all points on the same straight line). I believe there must be a kind of concatenation between the points but  I couldn't figure it out.

What I tried is totally mess. I tried to draw some triangles and to connect some points from one triangle to another, but in vain.

**Note:** I want to see a real example of such an infinite set of points in the plane that can be an answer for the question. A graph for these points would be helpful.