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.By Guillermo Bautista Jr. , Created with GeoGebra

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

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.

NoToolsInstructionsViewmenu to display the coordinate axes.Slidertool and click on theGraphics viewto display theSlider dialog box.Numberfrom the option buttons, and leave the other options as is. GeoGebra will automatically giveaas the slider name.bsimilar to slidera.