Perpendicular to a Line at an External Point

Given a line and a point not on that line, we will construct a perpendicular line through the given point.

Recall that points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment.  So we will mark off a segment whose endpoints are equidistant from the given point by drawing part of a circle centered at the given point.

Set the compass at any convenient length more than the distance from the point to the line, place the tip on the point and cut the line with part of the circle to mark the endpoints of segment AB:

 

Then construct the perpendicular bisector of segment AB: 

Here is an animation of this construction.

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