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.