Origin

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The origin of a coordinate system is the center point or zero point where the axes meet.

In Euclidean Systems

In the Euclidean plane $\mathbb{R}^2$, the origin is $(0,0)$. Similarly, in the Euclidean space $\mathbb{R}^3$, the origin is $(0,0,0)$. This way, in general, the origin of an $n$-dimensional Euclidean space $\mathbb{R}^n$ is the $n$-tuple $(0,0,\ldots,0)$ with all its $n$ components equal to zero.

Thus, the origin of any coordinate system is the point where all of its components are equal to zero.

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