Page 125 - MAT KS3 Y8 Cambridge CheckPoint

12.2 Drawing a perpendicular bisector

✦ Exercise 12.2

1 Follow these instructions to draw the perpendicular bisector of a line segment AB.
a Draw a line segment 8 cm long. Label one end A and the other end B.
Make sure you allow 6 cm of space above and below the line for drawing the arcs.
b Open your compasses to a radius that is more than half the length of AB.
c Put the compass point on the end of the line that is marked A. Draw a large arc.
d Put the compass point on the end of the line that is marked B.
Draw a large arc that crosses the other arc in two places.
e Join the points where the two arcs cross. Make sure you draw a straight line.
2 Follow these instructions to draw the midpoint on a line segment CD.
a Draw a line segment 5 cm long. Label one end C and the other end D.
Make sure you allow 4 cm of space above and below the line, for drawing the arcs.
b Open your compasses to a radius that is more than half the length of CD.
c Put the compass point on the end of the line marked C. Draw a large arc.
d Put the compass point on the end of the line marked D. Draw a large arc that crosses the other arc
in two places.
e Place your straight-edge along the line joining the points where the two arcs cross.
f Mark a dot where the straight-edge crosses CD.
g Check this is the midpoint. Use a ruler to measure the distance from C to the midpoint, and the
distance from D to the midpoint. They should both be 2.5 cm.
3 Work with a partner. You will each need a clean sheet of plain paper.
You should both draw the
a Draw a line segment EF. The line segment can be any length
line on your own paper.
between 4 cm and 14 cm long.
Make sure you allow plenty of space above and below the line for
drawing arcs.
b Exchange papers with your partner.
c Using only compasses and a straight-edge, draw the perpendicular bisector of EF on the paper
you have been given.
d Exchange with your partner again, so you now have your own paper back.
e Now use a ruler to check that your partner has draw the perpendicular bisector exactly through
the midpoint of EF.
f Use a protractor to check that your partner has drawn the perpendicular bisector at exactly 90°
to EF.
4 A builder buys a rectangular plot of land. A 100 m
The sketch shows the dimensions of the plot of land ABCD. B
a Using a ruler and protractor, draw an accurate copy
of the plot of land. Use a scale of ‘1 cm represents 10 m’.
80 m
b Using compasses and a straight-edge, on your diagram, find:
i the midpoint of AB ii the midpoint of BC.
c The builder is going to put a fence from the midpoint D C
of AB to the midpoint of BC.
Draw this fence on your diagram.

12 Constructions 123