
How to construct a line perpendicular to a given line, passing through a given point on this line?

1. 
 Start with two points defining the given line.


2. 
 Determine the given point.


3. 
 Draw a circle with point 2 as its center, and a suitable radius.


4. 
 Draw an arc with the center at one of the intersections of line 1 and circle 3, and a suitable radius, preferably somewhat greater than the diameter of circle 3.


5. 
 Repeat this for the other intersection of line 1 and circle 3. The radius must be equal to that of arc 4, and both arcs must intersect twice.


6. 
 Draw the line connecting both intersections of arcs 4 and 5.


7. 
 This is the line to be constructed, perpendicular to line 1 and passing through given point 2.

