Question

How do we construct the perpendicular bisector of a segment to find its midpoint?

Answer 1

Please see below.

Explanation:

The following way constructs the perpendicular bisector and also finds the midpoint of the given line segment.

Let us consider the line segment `AB`.

Now open a compass so that distance between tip of the needle and pencil tip is more than half the segment `AB`, preferably equal to segment `AB`. This distance isthe radius of any arc that can be drawn using compass

Now with center at `A` draw two arcs on both sides of the segment, so that they appear just above and below the segment `AB` as shown.

Do not change radius i.e. distance between tip of the needle and pencil tip and now draw two more arcs, now with `B` as center, so that they intersect the arcs drawn earlier.

The figure appears as shown below.

Now if we join the two intersection points of arcs, we get the perpendicular bisector of line `AB` and the point where it intersects the segment `AB` is the middle point of segment `AB`.