Reflection (y=x)
- Author:
- Roger Gemberling
For the first sketch, you will explore reflecting a triangle over line y=x. Here are some problems to complete:
(1) Move the vertices of the original triangle to (-1,1), (2,3) and (0,3). Now move the "gray" triangle so it represents the reflection of the original triangle. Click on the Reflection button to check your answer.
(2) Move the y=x line by moving the green point. As the line moves, how does the reflected triangle move? (You will get an opportunity to respond to this question later.) Hide the Reflection by clicking on the Reflection button and return the green point to (0,0).
(3) Move the vertices of the original triangle to (-1,0), (2,2) and (2,4). Now move the "gray" triangle so it represents the reflection of the original triangle. Click on the Reflection button to check your answer. Move the y=x line, how does the reflected triangle move? Hide the Reflection..
(4) Move the vertices of the original triangle to (-1,2), (1,3) and (-1,4). Move the y=x line so the green point is located at -1. Now move the "gray" triangle so it represents the reflection of the original triangle. Click on the Reflection button to check your answer. Move the y=x line, how does the reflected triangle move? Hide the Reflection.
(5) Move the vertices of the original triangle to (-1,2), (1,0) and (2,2). Move the y=x line so the green point is located at -1. Now move the "gray" triangle so it represents the reflection of the original triangle. Click on the Reflection button to check your answer. Move the y=x line, how does the reflected triangle move? Hide the Reflection.
(6) Spend another 5 to 10 minutes creating your own problems.
In the previous sketch, you were asked to consider the moment of the triangle as you moved y=x. Move the green point for y=x to create the path for possible vertices of the reflected triangle.
Did you identify the same path when asked earlier? Continue to the next activity to further explore this path.
Log into Desmos. You will have 5 problems to complete. Once you are logged in, you will complete the Desmos activity within this GeoGebra activity so you can look back at previous problems if it helps.
Now practice reflecting the triangle over the y=x line. Move the gray triangle to the correct place, then click on the Answer button. If you want to see the placement of one of the reflected points, click on the Hint button. Close either button before clicking on the Next Problem button.
This sketch will generate new problems for you, just click on Next Problem button. Continue practicing until you get 10 problems correct.