# Constructing a Perpendicular Line from a Point Not on the Line

How to construct a perpendicular line from a point that is not on the line.

## Goal

Goal:

Constructing the line

that is perpendicular to the given line

and that passes through the given point

which is not on the line.

## How to Construct

Place the point of the compass

at the given point.

(red point)

Draw two arcs

that intersect with the given line.

(red arcs)

Place the point of the compass

at one of the intersection

of the arc and the given line.

(red point)

Draw an arc

that is below the given point.

(red arc)

Without changing the radius of the compass,

place the point of the compass

at the other intersecting point.

(red point)

Draw an arc (red arc)

that intersects the previous arc (blue arc).

Draw a line

that passes through the given point

and the intersecting point formed by the arcs.

Then the vertical line is the line

that is perpendicular to the given line

and that passes through the given point

which is not on the line.