Let be a line containing the points and . Determine which of the following points are also on .

- ;
- ;
- ;
- ;
- ;

By Theorem 13.4 (page 474 of Apostol)we know that given two points there is a unique line between them which is the set of points

So, the set of points on are all points of the form for .

- The point is not on since there is no such that .
- The point is on since if we take then .
- The point is not on since for any .
- The point is on since if we take then .
- The point is on since if we take then .

Hi! Just want to let you know that for part b, I believe it is t = 3/4 instead of t = -3/4. Have a great day!