### From Wikipedia, the free encyclopedia

The origin of a Cartesian coordinate
plane

In mathematics,
the **origin** of a Euclidean space is a special point,
usually denoted by the letter *O*, used as a fixed point of
reference for the geometry of the surrounding space. In a Cartesian coordinate
system, the origin is the point where the axes of the system intersect. In Euclidean
geometry, the origin may be chosen freely as any convenient
point of reference.

The most common coordinate systems are two-dimensional
(contained in a plane) and
three-dimensional (contained in a space) systems, having two and three perpendicular axes,
respectively. The origin divides each of these axes into two
halves, a positive and a negative semiaxis. Points can then be
located with reference to the origin by giving their numerical coordinatesâ€”that is, the positions of their
projections along each axis, either in the positive or negative
direction. The coordinates of the origin are always all zero, for
example (0,0) in two dimensions and (0,0,0) in three.

## Symmetry with respect to
the origin

This graph is

**symmetric with respect to the origin**
because when reflected over both the x-axis and the y-axis, the
graph looks unchanged.

When a graph is symmetric with respect to the origin, it
describes a graph that looks the same before and after the graph is
rotated 180 degrees. Formally, a graph is symmetric with respect to
the origin if it is unchanged when reflected across both the x-axis
and y-axis.