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. 

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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