Constructing a Function
You have been given a piece of paper measuring 8.5 inches by 11 inches. Fold the paper so the top right corner (point D) falls somewhere along the bottom edge of the paper as suggested by point F along edge BC in the following sketch.
Find a function of the area of triangle EFC with respect to the length of segment FC. Plot the graph. Point P should trace your graph (if it doesn't, you'll need to revise your function). Once you have a working graph, explore relationships between FC and the area of EFC for various dimensions of paper.