Pantograph with GeoGebra

This is a simulation of the traditional pantograph which is used to enlarge figures.
In building a GeoGebra simulation, it is important to analyze the dependencies of the pantograph, as is important in all GeoGebra models. 1) How does understanding such dependencies help students approach the mathematics? 2) Why is the pantograph able to produce "proportional" enlargements? 3) Is it "always" mathematically proportional? What if you change the lengths of the relevant segments? 4) What is the ratio between AB and AP? 5) How is it related to the mathematical idea of dilation?