1. The problem statement, all variables and given/known data Let (A l b) be an element of E(2) (a) Show that (A l b) is a rotation if A is a nontrivial rotation (show that it fixes some point). (b) Show that (A l b) is a glide reflection if A is a reflection (find the line, not necessarily through the origin, that is taken into itself - draw a picture). (c) Conclude that every element of E(2) is a rotation, a glide reflection, or a translation. 2. Relevant equations 3. The attempt at a solution (a) A nontrivial rotation takes a vector that starts at the origin to another vector that starts at the origin. So (0,0) is the fixed point? The matrix first line: cos(theta) -sin(theta) second line: sin(theta) cos(theta)] is a rotation. So to show that (A l b) is a rotation , is A the matrix above, x a point in the plane E(2) and b the vector first line: 1 second line: 0?? I need to see this worked out so the light bulb will click!