Definition:Coordinate System/Origin

Definition
The origin of a coordinate system is the zero vector.

In the $x y$-plane, it is the point:
 * $O = \tuple {0, 0}$

and in general, in the Euclidean space $\R^n$:
 * $O = \underbrace {\tuple {0, 0, \ldots, 0} }_{\text{$n$ coordinates} }$

Thus it is the point where the axes cross over each other.