# Definition:Projection (Analytic Geometry)

Let $M$ and $N$ be distinct lines through the origin in the plane.
The projection on $M$ along $N$ is the mapping $\pr_{M, N}$ such that:
$\forall x \in \R^2: \map {\pr_{M, N} } x =$ the intersection of $M$ with the line through $x$ parallel to $N$.