Plane transformations (other)

Besides the basic plane transformations (translations, rotations, reflections, and dilations), there are other transformations that change the plane in different ways. Some examples include shears, glide reflections, and general affine transformations. These can move, stretch, or skew shapes in ways that are not just simple sliding, turning, flipping, or resizing.

Important properties

• Shear transformations slide parts of a shape parallel to a line, changing angles but keeping areas the same.

• Glide reflections combine a reflection with a translation along the direction of the mirror line.

• Affine transformations are combinations of linear transformations (like rotations, reflections, shears, and dilations) and translations.

• Some of these transformations preserve parallelism and ratios of lengths along parallel lines, but not necessarily angles or lengths.