# Construction: Midpoint of a Line Segment

How to construct the midpoint of a line segment (and the perpendicular bisector): by using a compass and a straightedge (ruler).

## Construction

Let's see how to construct

the midpoint of the given line segment.

Place the point of the compass

at the left endpoint of the line segment.

(blue point)

Draw two arcs

on the top and bottom of the segment.

Set the radius of the compass

that seems 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.

Draw two arcs

on the top and bottom of the segment.

Draw a line that passes through

the intersecting points

of the top arcs and the bottom arcs.

Then the intersection

of the vertical line and the given line segment

is the midpoint of the line segment.

And the blue line

is the perpendicular bisector of the line segment.