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

I think there is a typo in the line after ¨Let s = q, \ t = r. Then,¨

should be: P – qP – rP + qQ + rR is on M