Model for Descriptive Geometry by A. Jullien - Distance from a Point to a Line

Jullien, A. · ca 1880

Given point (a, a’) and line L, the slanted wire coming out of the horizontal plane at c and extending through (m, m’). Construct the horizontal line through (a, a’) that is perpendicular yet above to line L (the wire coming out of the vertical plane at d toward the right.) Then the plane FPF’ is a perpendicular to L at (m, m’). The vertical projection of the intersection of the plane and L is point e’ while the horizontal projection is point g. The red string is the line joining these two points which passes through (m, m’). Line eg is the horizontal projection of this line. By rotating points (a, a’) and (m, m’) about eg onto the horizontal plane, we get their images A’ and M’. The length of segment A’M’ is the distance from point (a, a’) to the line L at its perpendicular foot (m, m’).