The four isometries are translation, reflection, glide reflection, and rotation. It is interesting to note that the isometries form a group under composition. Furthermore, each isometry can be distinguished by its fixed point behavior and whether or not it preserves orientation. Below you will find brief descriptions of the isometries and illustrative animations. Keep an eye out for the distinguishing characteristics mentioned above.
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.