Reflections

A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage.

A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

Some simple reflections can be performed easily in the coordinate plane using the general rules below.

Reflection in the x-axis:

A reflection of a point over the x-axis is shown.

The rule for a reflection over the x-axis is .

Reflection in the y-axis:

A reflection of a point over the y-axis is shown.

The rule for a reflection over the y-axis is .

Reflection in the line y = x :

A reflection of a point over the line y = x is shown.

The rule for a reflection in the line y = x is

Reflection in the line y = -x :

A reflection of a point over the line y = – x is shown.

The rule for a reflection in the origin is .