Composition of Two Isometries, Rotation & Glide Reflection

[zhandele]

Homework Statement

R is a rotation around the origin by ∏/4, G is a glide reflection; the reflection is across y=x and the glide is by (2,2). Find the compositions R°G and G°R and characterize them. If you find a glide reflection, specify both the mirror line and the "glide" vector.

Homework Equations

See attachments ...

The Attempt at a Solution

Both of these seem to come out reflections followed by translations, but neither is a glide reflection (the glide isn't parallel to the mirror line). I'm confused about two things. First, the way the question is worded leads me to expect that at least one of these should be a glide reflection, but I can't see that either is. Again, in the case of R°G, if you look at the GSP results, the measurements don't jibe with my calculations. I really don't know how to account for this.

 

[boucher3200]

How do you verify that the matrix equation [x',y']=[0 1 0 1][x y] + [sqrt 2 sqrt 2] is a glide reflection along the diagonal y=x with a translation of 2 units in the northeast direction?