Double Reflection about Parallel Lines
- Author:
- Tim Brzezinski
- Topic:
- Algebra, Coordinates, Geometry, Reflection, Rotation, Translation, Vectors
In the app below,
- Use the LINE tool
to construct a line. - Use the REFLECT ABOUT LINE
to reflect Lisa's pic about this line. - Use the PARALLEL LINE tool
to construct a line that's parallel to the line you made in (1) above. - Reflect Lisa's image (you made in step (2) about the line you just created in (3).
5. Now right click on the first image you made in (2). Uncheck "Show Object". The only items that should be showing now are the original Lisa (preimage) and the image you made under the double reflection (in step 4).
Notice how we reflected about two parallel lines. Is there another single transformation that will take the original preimage and map it directly onto the final image (you made in step (4)). If so, what is it? Demonstrate how your response is true by completing this transformation in the app above.
If we reflect any image about a line and then reflect this image about any line parallel to the original line, the final resulting image can be obtained by carrying out a single transformation. Which transformation is it?