Not too sure what to do. Even a hint on how to start it would be appreciated. Thanks!

6. A and B are the points (-1, -3, 2) and (2, -1, 1) respectively.

B and C are the points of trisection of AD, that is AB = BC = CD.

Find the coordinates of D.

## 2003 P1 Q6

### Joel

Posted 01 May 2006 - 02:08 PM

Not too sure what to do. Even a hint on how to start it would be appreciated. Thanks!

6. A and B are the points (-1, -3, 2) and (2, -1, 1) respectively.

B and C are the points of trisection of AD, that is AB = BC = CD.

Find the coordinates of D.

Start by calculating vector AB. Since B and C are points of trisection then 3AB = AD. Use AB to calculate the components of AD, then find point D by making the equation d - a = AD and substituting point A (which you are already given) and vector AD into the equation. If you need further help please ask and I will post a full solution.
6. A and B are the points (-1, -3, 2) and (2, -1, 1) respectively.

B and C are the points of trisection of AD, that is AB = BC = CD.

Find the coordinates of D.