Projection onto a line

Given a point $P$ and a line $l$ in the plane, the projection of $P$ onto $l$ is the point $Q$ on $l$ such that the segment $PQ$ is perpendicular to $l$. This is called the orthogonal (or perpendicular) projection.

Important properties

• The projection is always the closest point on the line to the original point.

• If the point already lies on the line, its projection is itself.

• The projection divides the segment from the point to the line into two perpendicular parts: one along the line, one perpendicular.