# Constructing a Perpendicular Line from a Point on the Line

How to construct a perpendicular line from a point that is on the line.

## Goal

Goal:

Constructing the line

that is perpendicular to the given line

and that passes through

the given point on the given 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 two arcs

that is above and below the given point.

(red arcs)

Without changing the radius of the compass,

place the point of the compass

at the other intersecting point.

(red point)

Draw two arcs (red arcs)

that intersect the previous arcs (blue arcs).

From this part, it's like

constructing the midpoint of a line segment.

Draw a line

that passes through the intersecting points

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 on the line.