# Construction: Perpendicular Line from a Point on the Line

How to construct a line that is perpendicular to the given line and that passes through a point 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 on the line.

### Construction

Place the point of the compass

at the given 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 two arcs

on the top and bottom of the given point.

(blue arcs)

Without changing the radius of the compass,

place the point of the compass

at the other intersecting point.

Draw two arcs (blue arcs)

that intersect the previous arcs.

Draw a line that passes through

the intersecting points

of the top arcs and the bottom arcs.

The line should pass through

the given point on the line.

Then the blue line is the line

that is perpendicular to the given line

and that passes through

the given point on the line.