Given a line and a point A not on the line
open the compass a distance larger than the perpendicular distance from the point to the line, and scribe an arc intersecting the line at two points.
Call the two points B and C. Scribe arcs from B and C of the same radius on the other side of the line from A.
Call the point where the two arcs meet D. Draw AD.
AD is the line through A perpendicular to BC.
AD is perpendicular to BC.