Construction: Perpendicular Line from a Point Not on the Line

How to construct a line that is perpendicular to the given line and that passes through a point not on the line: by using a compass and a straightedge (ruler).

Example

Given

Let's see how to construct the line
that is perpendicular to the given line
and that passes through
the given point not on the line.

Construction

Place the point of the compass
at the given point.
(blue point)

Draw two arcs
that intersect with the given line.

Place the point of the compass
at the left intersecting point
of the arc and the given line.
(blue point)

Draw an arc
that is below the given point.
(blue arc)

Without changing the radius of the compass,
place the point of the compass
at the other intersecting point.

Draw an arc (blue arc)
that intersects the previous arc.

Draw a line
that passes through
the given point and the intersecting point of the arcs.

Then the blue line is the line
that is perpendicular to the given line
and that passes through
the given point not on the line.