Page 124 - MAT KS3 Y8 Cambridge CheckPoint

12.2 Drawing a perpendicular bisector

12.2 Drawing a perpendicular bisector

AB is a line segment. A B

The midpoint of the line segment is the point that is midpoint of AB
exactly halfway between A and B. A B

The perpendicular bisector of the line segment AB is perpendicular bisector of AB
the line that passes through the midpoint of AB at
A B
right angles to AB.
‘Perpendicular’ means ‘at right angles to’. ‘Bisect’
means ‘cut in half’.
Worked example 12.2 shows how to draw the midpoint
and perpendicular bisector of a line segment,
using only a straight-edge and compasses.

Worked example 12.2
PQ is a line segment. P Q
Draw onto PQ:
a the midpoint b the perpendicular bisector.

Step 1 Step 2
Open the Keep the radius of
compasses to a the compasses the
radius that is more same. Place the
than half the length compass point on
of the line PQ. other end of the
Place the compass line (P) and draw a
point on one end large arc.
P Q of the line (Q) and P Q
draw a large arc.

Step 3 Step 4
Place your straight- Hold the straight-
edge along the line edge still and draw
midpoint joining the points a straight line to
where the two arcs join the points
cross. Draw a dot P Q where the two
P Q
on the line to show arcs cross. This is
the midpoint. the perpendicular
bisector of PQ.

perpendicular
bisector

122 12 Constructions