Exploring Transformations
- Author:
- Patrick Eggleton
. Select your triangle (click and drag to get the whole triangle) and the line to reflect the triangle.
Explore by moving the vertices of your original triangle or by moving the reflection line. What is true of the reflection line in relation to any of the segments AA', BB' or CC' ?
From the transform menu, choose the "Translate object by Vector" tool 
. Choose the triangle and then the vector to translate the triangle. Measure the length of the vector and the distance between two vertices of your triangle. What do you observe?
In the sketch above, line ED and the line through F are parallel. Reflect the triangle first in ED and then reflect the image in the parallel line through F. Measure the distance between corresponding vertices in the original triangle and the final image. What single transformation will accomplish the composition of the two reflections? Move the lines around so you can be as specific as possible.
. Select the triangle and then the point D as the center for the rotation. Rotate the triangle by 75 counterclockwise. Construct two lines that intersect at D. Reflect the triangle over the line closest to the triangle and then across the second intersecting line. Try to arrange the lines so that the composition of reflections is the same as the rotation. Explore various measures related to the angles between corresponding vertices and the angles between the lines.What have you discovered about the composition of reflections in two intersecting lines and a rotation through the point of intersection of the two lines? Be as specific as possible.