Question

Explain why a plane cannot be named by any three points in the plane, but must be named by three noncollinear points in the plane.

Answer 1

A line can be defined simply with the use of two points - one for each end. In a similar way, a plane can be defined using three points. However, if each of the points are collinear - they will instead define a line. Therefore, three points defining a plane can be produced only by three non-collinear points. The plane will pass through these three points and in principle is infinite in extent.