Given a point on the line it is possible to use a compass and straightedge to create a line that is perpendicular to and that passes through This will be the unique line described by the Perpendicular Postulate.
First, place the sharp end of the compass at point
and draw a circle.
The circle intersects at two distinct points. These points will be named and for later referencing.
Place the sharp end of the compass at
and draw an arc above point
Next, using the same compass setting, the sharp end is placed at
and another arc is drawn above
such that it intersects the first arc.
By using a straightedge to draw a line through
and the intersection of the arcs, the desired perpendicular line is constructed.