Drawing perpendicular to a line through a point not on it – Using ruler and compass

Let’s take an example

1. Given a line l
   with point P not on it

2. With P as center, and any radius,
   draw an arc intersecting the line at points A and B
   
3. Now with A as center, and same radius  draw an arc.
   With B as center, and same radius as before, draw an arc

4. Mark the point of intersection of the two arcs as point Q

          Join P & Q.

∴ PQ is the line perpendicular to line l