The pivot point around which everything rotates doesn't move at all. Using the analogy of a square drawn on a large transparent sheet of plastic, you might do a rotation by holding down the pivot point with your finger, and whirling the sheet around it. This is worth pointing out, since it suggests a way of classifying any kind of isometry, by considering their fixed point behavior. In thinking about translation and rotation, we discovered that a useful question to ask about an isometry is whether or not it has fixed points , i.e. points that do not move. Translations have no fixed points, while rotations have exactly one, namely the pivot point around which everything else turns.
Reflections are isometries that have infinitely many fixed points.
We say that reflection is orientation reversing . One way of describing what it means for an isometry to be orientation reversing is to think of the square as being drawn on a large clear sheet of plastic laying on a white table top. To translate or rotate the square, you just have to slide the plastic sheet around on the table top. By contrast, to do a reflection, you have to pick up the sheet, and turn it over , before sliding the square into its final position. Another way of describing the difference between and orientation reversing and preserving transformations is that an orientation reversing transformation gives you back a mirror image of your original shape.