Composition of plane transformations

The composition of plane transformations means performing two or more transformations one after another on a figure in the plane. For example, you might first reflect a shape over a line, then rotate it around a point. The result is a new transformation that combines the effects of both.

Important properties

• The order of transformations matters: doing A then B can give a different result than doing B then A.

• Some transformations, when composed, can be replaced by a single transformation of the same or different type (e.g., two reflections over parallel lines equal a translation).

• The composition of two transformations is itself a transformation.