The Pantograph

A pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen. If a line drawing is traced by the first point, an identical, enlarged or miniaturized copy will be drawn by a pen fixed to the other. The pantograph was invented by Cristoph Scheiner.

The applet above demonstrates how the pantograph works.  Move the blue point (hinge) and draw any shape. 

Questions:
1.) What do you observe?
2.) What is the relationship between the blue figure and red figure?
3.) Justify your answer in 2.
4.) Prove that the relationship in 2 always holds.

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