Supplementary Investigation 22

The Image of a Circle Not Passing Through the Center of Inversion

Tool(s) Geometers Sketchpad

Data File(s) si22

Focus The image of a circle not passing through the center of inversion.

Tasks

1. Experiment with the drag pts and observe the effects they have on the positioning of objects and images and the calculations displayed. To obtain the correct image following any movement of the drag pts, you must move points R', r', P', p', Q', and q' so that their distances from O match their calculated positions. When you have correctly done so, what shape does the image appear to be?

2. Could you view the outside circle as the object and the inside circle as the image in this process? Would the construction permit you to reverse the roles of object and image in this way? Why or why not?

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