The intent of this worksheet is to show that you can transform any line segment into any other line segment, and that the function that will do so is itself a linear function. It looks like there is an interesting relationship between the direction of the original line-segment and how much it can be transformed from the original line segment, which suggests to me that my definition is incomplete.
I will next consider a model built on D = (a*x(C)+b*y(C)+c, d*x(C) + e*y(C) + f) using six different sliders. In any case, I will publish this first applet as an in between step.