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4.4 Exploration, example #4

Author:Ryan Fisher

Directions

For examples #3 & 4, use the applet to reflect the triangle over each of the intersecting lines. After, answer the questions to deduce a pattern for the generic case.
  1. Use the polygon tool to trace triangle ABC
  2. Use the line tool to construct the lines y = 0 and y = x
  3. Reflect triangle ABC over the line y = x
  4. Reflect the image over the line y = 0.
Note: although the lines are the same, the order in which you performed the reflections is not the same. This will change the final image, so if you have the same final picture as example #3, go back and make sure you have read the directions thoroughly.

Example #4

Analysis

  1. What transformation occurred that would map the pre-image directly to the final image (without needing to do the reflection in the middle)?
  2. What is the magnitude (size) of that transformation?
  3. In what direction is this transformation?
If it helps, use this table of values to keep track of the coordinates after each reflection.
Image

Conclusion

Use your results from examples #3 and 4 to answer the following questions:
  1. What transformation is the same as a double reflection over intersecting lines?
  2. What is the connection between the size of the angle made by the intersecting lines and the magnitude of the transformation?
  3. How do you find the direction of the final transformation?
Write your answers to these questions in your notebook.

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