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.