An isometry of the plane is a linear transformation which preserves length. Isometries include rotation, translation, reflection, glides, and the identity map. Two geometric figures related by an isometry are said to be geometrically congruent (Coxeter and Greitzer 1967, p.

Does isometry preserve orientation?

The order in which the vertices of a figure appear is called the orientation of the figure. ... A direct isometry is an isometry that preserves orientation (the order of the vertices). An opposite isometry is an isometry that changes the order of the vertices from counterclockwise to clockwise or vice versa.

Does isometry preserve size?

An isometry will not change the size or shape of a figure. I can phrase this in more precise mathematical language. The image of an object under an isometry is a congruent object. An isometry will not affect collinearity of points, nor will it affect relative position of points.