Let be three points in not all on the same line, and let be the plane they determine.
- If with prove that the point is on .
- Prove that all of the points on are of the form for with .
- Proof. Since is the plane determined by the three points we know is the set of points
Let . Then,
- Proof. Let be a point on . Then, we know there exist such that
But, ; thus, for