Supplementary Investigation 21

The Image of a Point Under Inversion

Tool(s) Geometers Sketchpad

Data File(s) si21

Focus Two points P and Q are inverse points with respect to a point O and a given positive real number r if OP*OQ = r², O, P, Q are collinear, and r is the radius of inversion.

Tasks

1. Use the measure menu to find the distances from O to Q, O to P, and the length of the radius of inversion.

2. Use the Calculate option in the Measure pull-down menu to find OP*OQ and the square of the radius of inversion.

3. Finally, move the 'P&Q drag pt.' around the circle, changing the distances of P and Q from O. Discuss your observations.

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