Translation has no fixed points and preserves orientation. The reflection map is, for the most part, self-explanatory. Glide Reflection Glide reflection is a combination of the above two isometries. Given any line in the plane, the mapping translates the points a given number of units in the direction parallel to the line. The points are then reflected over the line.
Glide reflection has no fixed points and is orientation reversing.
The rotation mapping is also self-explanatory.