Transformations that are rigid motions are also called isometries. They preserve size and shape.
Rigid Motions:
Translation
Rotation
Reflection
There's often another one called a
Glide Reflection
which is a combination of translation and reflection.
Not Rigid Motions:
Dilation
Obviously dilations change the size. There are also transformations that distort the figure, for example scaling the coordinates differently. Let's call them:
