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.

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

geometry-point-perpendicular
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.