\begin{definition}[Definition:Point at Infinity/Homogeneous Cartesian Coordinates/Point on Line]
Let $\LL$ be a straight line embedded in a cartesian plane $\CC$.
Let $\LL$ be given in homogeneous Cartesian coordinates by the equations:
:$l X + m Y + n Z = 0$
The '''point at infinity''' is expressed in homogeneous Cartesian coordinates by an ordered triple in the form:
:$\tuple {-m, l, n}$
\end{definition}