Exercise 1. Let f = Opeo Oq, where 0, (0, 2). Show that fis the identity if p = q and = 2 - 0, a translation if p q and = 2-0, and a rotation otherwise. Hint: in class, we argued that the composition Reo Re of two reflections through lines l, l' that intersect at a point p is a rotation around p by an angle that's twice the angle from l' to l. So, any rotation Ope can be written as a product Reo Re of two reflections, and you can even choose & to be any line through p as long as you then choose l' appropriately.