§ 10.7
Given three non-parallel lines a, b, and c in the plane that intersect in a single common point P, construct a line l so that the product of the reflections in the three given lines is the reflection in l, i.e.,
| sigma_{c} \circ sigma_{b} \circ sigma_{a} = sigma_{l} . |
Let rho be the rotation of the plane about the point P through the angle theta and tau the translation of the plane by the vector V. Relative to the given objects P, V, and theta, provide a geometric description of:
rho tau rho^{-1}.
tau rho tau^{-1}.
A rotation of the plane is determined by specifying a point as its center and an angle. Relative to that method of description explain how the composition of two given rotations about different centers may be constructed.