Cartesian coordinate system

Summary

A Cartesian coordinate system in the Euclidean plane is a choice of a unit of length and of two perpendicular directed lines, the axes. The axes meet at a point $O$, the origin. Each point $P$ then has a unique pair $(x, y)$ of real numbers, its coordinates. The numbers $x$ and $y$ are the signed distances from the origin to the perpendicular projections of $P$ on the two axes. In a Euclidean space of dimension $n$, a Cartesian coordinate system has $n$ mutually perpendicular axes through one origin, and each point has $n$ coordinates. The map from a point to its coordinates is a bijection onto $\mathbb{R}^n$ that keeps distances.