SOLUTION= After drawing the line segment mark point A and point B on the two ends of the line segment and take a pair of compass and stretch its length to be more than half the line segment but less than the line segment. From point A make a circle, from point B make a circle, both the circles should intersect at two points. Join the points with a line segment, this is how to make a perpendicular bisector of a line segment.
NOTE= I have used a circle too be accurate.
Hope this helps!