Construct a Perpendicular Line through Another Line Using a Compass

By Mark Ryan

Say you’re given a line with a point somewhere along it, and you have to construct a second line perpendicular to the first one through that point. Can it be done? Absolutely! The following example will show you how.


As you work through this construction, you can refer back to this figure:

Constructing a perpendicular line through a point on a line.
  1. Using any radius r, construct arc (W, r) that intersects line EF at X and Y.
  2. Using any radius s that’s greater than r, construct arc (X, s) and arc (Y, s) intersecting each other at point Z.
  3. Draw line WZ.

That’s it; line WZ is perpendicular to line EF at point W.