This seems like a long lab, but the essential parts are (1) the tools in part A, which are then used to repeat some of the work of this morning's 445 class and (2) the plotting sketches in Part B. The figure in Part C will be on Assignment 1, and this suggests ways to use Sketchpad to help answer the questions. But it is up to you whether you use GSP heavily or relvy more on working on paper.
Part A. Coordinates in the Plane
Use GSP to computer C-height of P with base AB. Compute 3 trilinear (or barycentric) coordinates in the plane to locate P.
Part B. Plotting Points from Coordinates
Given two of the 3 trilinear coordinates, construct P. Also construct lattices related to triangle ABC.
Part C. A triangle figure with everything
A point P inside a triangle generates points on the sides by constructing parallels and also by constructing lines through P and the vertices. The ratios of lengths are closely related to the barycentric coordinates.