ReflectRotate

This applet shows the result of first reflecting x to get x', and then rotating x' around P by the angle shown to get x''.

There are 3 things I think you might want to investigate, and there are things you can show to help with each:

If you reflect and then rotate, do you always get something that can be achieved by a single reflection across another line? The first set of hide/show buttons lets you show another reflection and its reflection line. If this is not always true, what circumstances make it true? If it is always true (and even if it isn't), can you describe how the two reflection lines and the angle and point of rotation are related?
If you reflect, then rotate, do you always get something that can be achieved by a glide reflection? If this is not always true, under what circumstances is it true? Describe how the reflection line, angle and point of rotation, and the glide reflection vector are related when it is true.
If you reflect ang then rotate, do you always get something that can be achieved by rotating and then reflecting? If not, under what circumstances is it true? Describe how the reflection lines, rotation points and rotation angles are related when it is true..