Perpendicular Bisector Construction
Grade 4What you are constructing
The perpendicular bisector of a line segment is a line that cuts through the midpoint at exactly 90°. Every point on this line is equidistant from the two endpoints. That property is what makes it so useful in loci problems.
Step-by-step construction
1. Set your compass to more than half the length of the line segment.
2. Place the compass point on one end of the line and draw an arc above and below the line.
3. Without changing the compass width, repeat from the other end. The two arcs cross in two places.
4. Draw a straight line through the two crossing points. That line is the perpendicular bisector.
Leave your construction arcs visible — examiners look for them to award the method marks.
In loci problems
EXAMPLE
Two towns A and B are 8 cm apart on a map. A new school is to be built so it is equidistant from both towns. Describe the locus.
The locus is every point the same distance from A as from B. That is the perpendicular bisector of line segment AB. Construct the perpendicular bisector — the school can be placed anywhere on the perpendicular bisector of AB.
