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

Jullien, A. · ca 1880

Suppose one is given plane APA’ and point (m, m’) not on the plane. To find the distance, one must find the perpendicular from the point to the plane. This is done by finding the shortest vertical and horizontal distances from the point to the plane. Segment mn on the horizontal plane is the projection of the shortest distance of point (m, m’) to the plane horizontally, often referred to as the perpendicular foot. Line de’ (red string) is the image of this foot up onto the plane. Likewise, segment m’n’ is the vertical perpendicular foot and its image on the plane is the wire coming out of the horizontal plane. Point (n, n’) where these two lines meet is the perpendicular from (m,m’) to the plane, and thus the shortest distance.