Definition:Coordinate System/Origin

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

In the $xy$-plane, it is the point:
 * $O = \left({0, 0}\right)$

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

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