Affine Barycentric Practice Problem

The figure shows a lattice made up of congruent parallelograms. Let (x, y, z) be the barycentric coordinates of a point with respect to the reference triangle ABC.

• Find the barycentric coordinates of each of the labeled points.
• Find the area of the triangle ABX (relative to the area of ABC), where X is any one of the labeled points. Do this for each labeled point in turn.
• Let S be the intersection of lines CE and BF.  What are the barycentric coordinates of S?
• Let T be the intersection of lines AQ and BC.  What are the barycentric coordinates of T?  What is the ratio BT/TC?
• Let U be the intersection of lines BR and CA.  What are the barycentric coordinates of U?  What is the ratio CU/UA?