Perpendicular to a Point on a Line

How to construct a Perpendicular to a Point on a Line
using just a compass and a straightedge

Steps to Construct

1. Place the compass point on the given point P
2. Draw an arc on both sides of P, cutting the line at two points (let's call them A and B)
3. Open the compass wider (it must be wider than the distance from A to P)
4. Place the compass point on A and draw an arc above the line
5. Without changing the compass width, place the compass point on B and draw another arc that crosses the first one at point Q
6. Use your straightedge to draw a line through P and Q

That's it! The line PQ is perpendicular to the original line at point P.