Perpendicular to a line from a given point

If you have a line segment and want to draw a perpendicular to it from a given point, you can do this with a compass and a straight edge.

Here is a point and a line segment. We want to draw a perpendicular line to the line segment.

Put your compass point on the point and mark two arcs that cross the line segment

You don’t need to draw the whole circle, just the arcs that cross the line segment, like this

Now we are in the same situation as creating a perpendicular bisector for a line segment but the line segment we are going to bisect is the one between the two arcs. Also, we already have the point above the line and need only create the point below using a compass.

We only need to mark the arcs of the circle that are approximately below the point above the line, like this:

Now we just use our straight edge to join a line segment between the point and our original line segment by putting the straight edge on the crossed arcs and the point. The two line segments meet at .