# 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).

## Construction

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.

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.