Supplementary Investigation 26

Analytic Geometry and Inversion

Tool(s) Geometers Sketchpad

Data File(s) si26

Focus The image of a straight line not through the center of inversion, under the transformation of inversion, is a circle passing through the center of inversion. The equations for the inversion transformation of a point P(x,y) into P'(x',y') relative to the circle centered at the origin are: X' = XR² / (X² + Y²) and Y' = YR² / (X² + Y²)

Tasks

1. Find the coordinates of P1, P2 and P3 with coordinate tool under the measure menu.

2. Use the Calculate option in the Measure pull-down menu to find P1', P2' and P3'.

3. Use the Plot tool in the Graph pull-down menu to plot these new points.

4. Use the Arc Thru 3 Points tool in the Construct pull-down menu to plot the image circle.

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