Translating a given line to infinity

In projective geometry, every line in the plane can be mapped to the 'line at infinity' using a projective transformation. This means we can choose a transformation that sends all points on a given line to points at infinity, making that line behave like the horizon in perspective drawing.

Important properties

• Projective transformations can move any line to the line at infinity.

• The line at infinity contains all 'points at infinity'—directions of parallel lines in the affine plane.

• After translating a line to infinity, lines parallel to the original line become parallel to the horizon (line at infinity).