# Seitz Symbol & E(2)

1. Aug 8, 2011

### 83956

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!