Construct a Line Perpendicular to Another Line Through a Point

By Mark Ryan

Say you’re taking a geometry test, and one question gives you a line along with a point that is not on that line. You’re told to construct a line perpendicular to the given line that also passes through the point.


Can it be done? Well, yes—but you’ll need a compass to make it happen.

The following figure will help guide you through a construction.

Constructing a perpendicular line through a point not on a line.

Now, follow these steps:

  1. Open your compass to a radius r (r must be greater than the distance from J to line AZ), and construct arc (J, r) intersecting line AZ at K and L.
  2. Leaving your compass open to radius r (other radii would also work), construct arc (K, r) and arc (L, r)—on the side of line AZ that’s opposite point J—intersecting each other at point M.
  3. Draw line JM, and that’s a wrap.