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4.4 Exploration, example #3

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 = 0
  4. Reflect the image over the line y = x.

Example #3

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
All of these questions could be predicted just by knowing this is a double reflection over intersecting lines. Make a conjecture (guess) that predicts each of these answers based on the starting information. Test your conjecture by completing example #4.