Q : Prove that a conjugate of a glide reflection by any isometry of the plane is again a glide reflection, and show that the glide vectors have the same length.
I know that:
the conjugate of a reflection by a translation (or by any isometry, for that matter) is another reflection, by some explicitly calculation (haven't try).
And 3 reflections leads to glide.
So I was thinking write a glide as 3 reflections and using the same process as proving 1 to prove the statement here. Is this promising? Can someone tell me? Or, should I try other methods?
Feel like this question is worth thinking. Thanks in advance~