Perpendicular through a Point off a Line

How to construct a line perpendicular to a given line,
passing through a given point not on this line?

1. Start with two points defining the given line.

2. Determine the given point.

3. Draw an arc with its center at point 2 and a suitable radius. The arc must intersect line 1 twice at points with a suitable distance.

4. Draw an arc with its center at one of the intersections of line 1 and arc 3, with a suitable radius.

5. Repeat this for the other intersection. The radius must be equal to that of arc 4, and both arcs must intersect at the opposite side of line 1 relative to point 2.

6. Draw the line connecting point 2 to the intersection of arcs 4 and 5.

7. The part of line 6 from point 2 to the intersection of it with line 1 is the line to be constructed, perpendicular to line 1 and passing through point 2.


Copyright © 2001, Zef Damen, The Netherlands