\begin{definition}[Definition:Homogeneous Cartesian Coordinates]
Let $\CC$ denote the Cartesian plane.
Let $P = \tuple {x, y}$ be an arbitrary point in $\CC$.
Let $x$ and $y$ be expressed in the forms:
{{begin-eqn}}
{{eqn | l = x
      | r = \dfrac X Z
}}
{{eqn | l = y
      | r = \dfrac Y Z
}}
{{end-eqn}}
where $Z$ is an arbitrary real number.
$P$ is then determined by the ordered triple $\tuple {X, Y, Z}$, the terms of which are called its '''homogeneous Cartesian coordinates'''.
\end{definition}