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 pointsLet . Then,

since implies

*Proof.*Let be a point on . Then, we know there exist such thatBut, ; thus, for