Plane transformations

A plane transformation is a function that assigns to every point $(x, y)$ in the plane a new point $(x', y')$. Transformations can change the position, orientation, or size of figures, but each point has exactly one image.

Important properties

• Transformations can be rigid (distance-preserving, like translations, rotations, reflections) or non-rigid (like scaling or shearing).

• Some transformations preserve angles, lengths, or parallelism.

• Transformations can be combined (composed) to create new transformations.

• The set of all plane transformations includes many familiar geometric operations.