Construction and Loci
Go to the BBC bitesize website: http://www.bbc.co.uk/schools/gcsebitesize/maths/
1. click on: geometry and measures
2. click on: loci
3. click on: Activity – this will give you an overview of what a locus is and how to draw the locus (a line) that is
at an equal distance from two points (perpendicular bisector).
4. click on: Revise
Note: bisect
Work through all pages making notes on loci and how to construct:
means cut in half.
 The locus of a set distance from a point
 A perpendicular bisector (same as in activity)
 A line that bisects an angle
 Triangles given three lengths – e.g. a triangle with side lengths of 6cm, 5cm and 4cm
 Triangles with one length and two angles – e.g. one 6cm side, and two angles of 55° 70°.
Loci for you to try:
On plain paper, construct the following using a ruler and compasses:
1. Draw two points, P and Q that are 8cm apart.
Draw the locus of points that are equidistant from P and Q.
P
8cm
Q
2. Draw two lines AB and BC so that the angle ABC is and acute and greater than 45o. Draw the locus of points that
are the same distance from AB and BC.
3. The diagram shows a plan view of the walls of a shed.
A goat is tied outside the shed to the corner G by a rope that is 3m long.
Use a scale of 2cm = 1m to make a scale
drawing of the shed and show the area that the goat can reach.
4. The diagram shows a triangular field ABC.
a) Use a ruler and compasses to construct a scale drawing of
the field using a scale of 1cm = 2m.
b) Draw the perpendicular bisector of AB
2m
G
4m
A
c) Bisect the angle ABC
d) construct the locus that is 12m from C
e) A telephone mast is to be placed in the field.
It must be:
 nearer to BA than BC.
 nearer to B than A
 more than 12m from C.
Shade the area where the telephone mast could go.
Additional practice: Edexcel 16+ book pg. 158 Ex. 15A-C
14m
B
20m
12m
C