Hey wall, I'm in collge geometry and my professor gave us practice problems before the final and I have some lingering questions regarding isometries. I'm in abstract algebra so I know that isometries are a groupd under composition.
1. Could a glide reflection followed by a rotation be a reflection?
2. Let Mx denote reflection in the x axis and let My dwnote reflection in the y axis. Show that Ro(180)◦Mx=My
1. My instinct is to say no because a glide reflection translates a point and then reflects, so if you rotate that point is still translated and cannot be a reflection.
2. By factoring Ro(180) into two reflections I get (My◦Mx)◦Mx therefore after re associating I ge the identity and then My. Correct?
Help is greatly appreciated.