Isometries: Rotation

régua e esquadro

A rotation transforms a object into another object. We see that rotating an object does not change the shape or size of the object. Therefore, a rotation transformation is an isometric transformation. In other words, a rotation is an isometry. To define a rotation, we must know the center and the measure of the rotation angle.

Created with GeoGebra by Vitor Nunes


You can change the value of angle `alpha` and observe that the figure is "rotating" around the center.

In this exercise the point `(0,0)` corresponds to the center of rotation of triangle [ABC]. The angle `alpha` represents the measure of the rotation.

Isometries of the plane

Bloco de notas

All plane isometric transformations can be expressed as compositions of a maximum of three mirror reflections. This fact allows the complete classification of plane isometries. Besides identical transformation, isometric transformations also include mirror reflection, translation, rotation around the center, and glide deflection.