# Constructing the Midpoint of a Line Segment

How to construct the midpoint of a line segment (and the perpendicular bisector of a line segment).

## Goal

Goal:

Constructing the red point

the midpoint of the given line segment

## How to Construct

Place the point of the compass

at the endpoint of the line segment.

(red point)

Draw two arcs at the upper part

and the lower part of the segment.

(red arcs)

The radius of the compass has to be larger than

one half the length of the segment.

Without changing the radius of the compass,

place the point of the compass

at the other endpoint of the line segment.

(red point)

Draw two arcs (red arcs)

that intersect the previous arcs (blue arcs).

Draw a line that passes through

the intersecting points formed by the arcs.

Then the intersection

of the vertical line and the line segment

is the midpoint of the line segment.

(red point)

And the vertical line

is the perpendicular bisector of the line segment.

(blue line)