How do I find the perpendicular of a line?

Answer 1

Using only a compass & straight edge (classic style), draw a circle around any point on the line. All you need is the two tiny arcs crossing the line. Then taking the two places where your first arcs crossed the line as centers, draw two bigger circles around those points. Note that each circle will each cross the line at two points. You actually need just the two points from each center "toward" the other center. (Don't make the two second circles so big that the radius is greater than the distance between the two points (though this will still work). This will give you two arcs across the line, and they will intersect each other above and below the line. If you then take your straight edge and draw a line through your original line from one of those intersections to the other, this new line will be perpendicular to the original line.

Use the link to the Wikipedia article and look at the construction. It's actually the construction of a perpendicular through a line from a point off the original line, but check it out and note the green arcs, which would be your two second arcs from the two centers you found with your first circle. The blue line is the perpendicular to the original (the black) line.

m2=-1/m1 where m1=grad of the original line & m2=grad of the line perpendicular to the original line