
Start with a line and point R which is not on that line. 

Step 1 
Place the compasses on the given external point R. 

Step 2 
Set the compasses' width to a approximately 50% more than the distance to the line.
The exact width does not matter. 

Step 3 
Draw an arc across the line on each side of R, making sure not to adjust the compasses' width in between.
Label these points P and Q 

Step 4 
At this point, you can adjust the compasses' width. Recommended: leave it as is.
From each point P,Q, draw an arc below the line so that the arcs cross. 

Step 5 
Place a straightedge between R and the point where the arcs intersect.
Draw the perpendicular line from R to the line, or beyond if you wish. 

Step 6 
Done. This line is perpendicular to the first line and passes through the point R. It
also bisects the segment PQ (divides it into two equal parts) 
