Constructions involving loci
1.
Construct an angle ABC of 60°. Construct the locus of points equidistant from AB and
BC.
2.
A and B are two points such that AB = 9cm. Construct the locus of points equidistant
from A and B.
3.
A and B are two points such that AB = 8cm
a) Construct the locus of points that are 3cm from A.
b) Construct the locus of points that are 2cm from the line AB.
c) In how many points do these loci intersect? How far is each point from B?
4.
Two straight lines AXB and CXD intersect at X such that angle AXC = 90°.
a) Construct the locus of points that are 4.5cm from X.
b) Construct the locus of points equidistant from AXB and CXD.
c) In how many points do these loci intersect? How far is each point from X?
5.
Draw a line AB that is 10cm long. Construct the locus of a point P such that triangle
ABP is isosceles with AP=BP.
6.
Construct a triangle ABC in which AB = 10cm, AC = 9cm and BC = 8cm.
a) Construct the locus of points equidistant from A and B.
b) Construct the locus of points equidistant from B and C.
c) Describe the point of intersection, O, of the loci you have drawn in (a) and (b).
d) Draw a circle, centre O, radius OA. (This is the circumcircle of ABC, O is the
circumcentre.)
7.
Draw a line AB that is 8cm long. Construct the locus of a point C such that angle ACB =
90° (C may lie on either side of AB).
8.
Construct a rectangle ABCD such that AB = 12cm and BC = 8cm.
a) Draw the locus of points equidistant from AB and BC.
b) Draw the locus of points equidistant from A and B.
c) Mark the point P that lies on the loci referred to in both (a) and (b). Measure PC.
9.
Construct a rectangle ABCD such that AB = 10cm and BC = 8cm.
a) Draw the locus of points equidistant from AB and CD.
b) Draw the locus of points, within the rectangle, that are 8cm from C.
c) Mark the point E, that is both equidistant from AB and CD, and 8cm from C.
Measure AE.
10.
Draw a line AB that is 8cm long. Construct the locus of a point P such that the area of
triangle ABP is 24cm2.
11.
Construct a triangle ABC in which AB = 12cm, AC = 11cm and BC = 8cm.
a) Draw the locus of points equidistant from AB and AC.
b) Draw the locus of points equidistant from AC and CB.
c) Mark, with X, the point of intersection of the two loci you have found in (a) and
(b). What is special about the point X?
12.
̂ C=30°.
̂ C=45° and BA
Construct a triangle ABC in which AB = 13cm, AB
a) Draw the locus of points that are 2.5cm from BC.
b) Draw the locus of points that are 1.5cm from AB.
c) Hence find the point, P, within the triangle, that is 2.5cm from BC and 1.5cm from
AB. Measure AP.