Higher Geometry I Quiz #4 Fall 2009

Name ___________________________

For each of the four types of motions of the Euclidean plane, it is possible that one or more points may be left unchanged by the motion (these are called fixed points or invariant points). For each of the types of motion, describe the set of fixed points for that motion.

(a) a translation
(b) a rotation with center O
(c) a reflection around the line m
(d) a glide reflection, which is not a reflection, based on the line m

Solution:

(a) a non-identity translation has no fixed points. The identity fixes all points.

(b) a non-identity rotation fixes only the center O. The identity fixes all points.

(c) each and only the points on the axis m are fixed by a reflection.

(d) a (proper) glide reflection has no fixed points