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GeoGebra

4.4 Exploration, example #1

Author:Ryan Fisher

Directions

For examples #1 & 2, you will perform a double reflection over two lines that are parallel to each other. Use the applet to perform the given double reflection. After, answer the questions to deduce a pattern for a generic double reflection over parallel lines.

Example #1

  1. Trace over the triangle with the polygon tool
  2. Trace each line using the line tool
  3. Reflect the triangle over the line x = -3
  4. Reflect the image over the line x = 2

Things to consider

  1. What transformation could you have done to go directly from the pre-image to the final image without doing the middle reflection?
  2. What was the magnitude (size) of that transformation?
  3. What direction was the transformation?
All of these questions could be predicted just by knowing this is a double reflection over parallel lines. Make a conjecture (guess) that predicts each of these answers based on the starting information. Test your conjecture by completing example #2.

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