In mathematics, an axis is a line with different meanings depending on the context. In a coordinate system, the axes are the reference lines (named the x- and y-axis) that form the coordinate plane. In the context of symmetry and rotation, an axis is the line that the object is reflected or rotated about.

Axis of a coordinate system

In coordinate geometry an axis (plural axes) is a reference line in a coordinate system. The intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, forms a two-dimensional coordinate plane, or the xy-plane shown below.

Axis of symmetry

An object or figure has an axis of symmetry or line symmetry if it can be reflected across a line back onto itself. The line that the object or figure is reflected across is an axis of symmetry.

In the figure above, the red line drawn through the butterfly is an axis of symmetry. Parallelogram ABCD is reflected across axis m to parallelogram (ABCD)'.

Axis of rotation

The axis of rotation is the line that an object or figure rotates about.

In the figure above, a plane is rotated counterclockwise around a line, called the axis of rotation. A wheel is an example of a common everyday object that rotates around its axis.