# Construct a Line Perpendicular to Another Line Through a Point

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.

Now, follow these steps:

**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.***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.***Draw line***JM,*and that’s a wrap.