Movement of a figure about a fixed point, at a given angle, often expressed in degrees. The angle is called the angle of rotation.

Transformation of a plane defined by a fixed point

*O*, called the “centre of rotation”, and a real number*α*, called the “angle of rotation”. This transformation maps a point*P*to a point*P’*so that segments*OP*and*OP’*are congruent and the measure of the angle formed by rays*OP*and*OP’*is the absolute value of*α*.### Properties

- A rotation is defined by a fixed point called the
**centre of rotation**and a**angle of rotation**. - Rotations may be used to create frieze patterns and tessellations.
- A rotation in a clockwise direction is a
**negative rotation**. - A rotation in a counterclockwise direction is a
**positive rotation**.

The invariants under a rotation of the plane are the following :

- The lines that map the rotation;
- the centre of rotation, which is a fixed point.

Rotations preserve:

- the perimeter and area of plane figures;
- the measures of angles;
- the alignment of the points;
- the orientation of the plane, since a rotation is a direct isometry.

A rotation does not preserve parallelism between a segment and its image.