For this lab, you will need a couple of tools. Also, you should be familiar with the last part of Lab 6 and the questions that were asked in that lab an in Assignment 6C.
Tool #1 -- Trilinear or Barycentric Coordinates from a triangle and a point P
This tool takes 4 points A, B, C, P and produces 3 numbers: x(P), y(P), z(P).
These numbers are the 3 ratios that were studied in the lab and the homework. The idea is that the triangle ABC is a reference frame for locating point P. The 3 numbers tell where P is located when be know the triangle.
As it turns out, if we parallel project a triangle ABC and a point P to get image points A' B', C' and P', the new point will have the same x, y, z with respect to A'B'C' as the point P had with respect to ABC.
Note that always x + y + z = 1, as you saw in the homework.
The numbers x, y, z are called the barycentric (or trilinear) coordinates of P with respect to triangle ABC.
How to make the tool:
Make a tool that takes A, B, C and P and produces this ratio. You can call this z or you can have the tool produce a label that says something like A(P) if you read in Sketchpad Help the section on Advanced Topics: Advanced Tool Topics: Generating Specific Labels
Check your work by calculating x + y + z. This should be 1 wherever P goes, including P OUTSIDE the triangle.
If this checks out, you can also make a tool that will construct all 3 measures at once. Or you may prefer to work with one at a time with the first tool above.