Definition:Point at Infinity/Homogeneous Cartesian Coordinates/Point on Line

Definition
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:


 * $\tuple {-m, l, n}$

Also see

 * Point at Infinity of Intersection of Parallel Lines, which justifies this construction