Flip of a figure about an axis

The axis

*d*that is perpendicular to a given direction.The axis

*d*is called the line of reflection.Symmetry about an axis

*d*perpendicular to a given direction.

The axis

*d*is called the line of reflection.

- The term “reflection” is a synonym for orthogonal symmetry.
- Frieze patterns and tessellations can be created by applying reflections.

### Notation

A reflection is often denoted by the letter “r”. A subscript may also be added to represent its axis. For example : *r _{d}* refers to a reflection

*r*across an axis

*d*.

### Properties

The invariants under a reflection in a plane are as follows:

A reflection also preserves:

- the perimeter and area of plane figures;
- the measures of angles.

The orientation of a plane is not preserved under a reflection, since a reflection is a flip that reverses the orientation of the plane.