Any shapes in the plane may end up in a different location, but they will not be distorted.

- Stretch
- Rotate
- Reflect
- Shear
- Project

Plus, the affine transformation:

- Translate

To decide which of these transformations are rigid motions, we just have to check whether or not they

Translations

Reflections

Rotations are described by their

Reflections are described by their

Translations are described by a direction and distance to move. They can be described by vectors.

Reflections and rotations have fixed points, translations do not.

The fixed points of a reflection lie along its *reflection axis*, the line it's reflected across. This line always goes through the center of the image.

Rotations have only one fixed point, in the center of the image.

Rotations and translations are orientation preserving, reflections are not.

Another named motion is really a combination of two others: a

This is a reflection combined with a translation (in either order).

Motion | Described By | Fixed Points | Orientation Preserving? |
---|---|---|---|

Rotations |
Center, Angle | One Point, Center | Yes |

Translations |
Distance, Direction | None | Yes |

Reflections |
Axis of Reflection | Along axis | No |

Glide Reflection |
Axis, Distance | None | No |