11 Qualitative Treatment of Locus
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Activity 11.1 (p. 3)
2.
1. (a)
The locus of P is made up of two parallel line segments, each at a distance of 1 cm from XY , with two semi-circles each of radius 1 cm, with centres X and Y respectively.
3.
(b)
2. (a)
(b)
p. 9
1.
The locus of P is a circle with centre O and radius 2 cm. p. 16
The locus of P is made up of three line segments, each at a distance of 1 cm from the triangle, with three one-thirds of a circle, each of radius 1 cm, centred at A , B and C respectively.
1. The locus of P is a straight line parallel to CD .
2. The locus of P is a smaller circle which lies inside the given circle.
3. (a) The locus of P is a straight line passing through A and P .
(b ) The locus of Q is a straight line passing through A and Q .
4. (a) The locus of P is a smaller circle which lies inside the given circle.
(b) no
5. (a) The locus of P is a smaller circle which touches the given circle internally.
(b) The locus of Q is a smaller circle which touches the given circle internally.
(c) no
Exercise 11A (p. 9)
Level 1
1.
1

Certificate Mathematics in Action Full Solutions 5A
2.
The locus of P is made up of two parallel line segments, each at a distance of 2 cm from MN , with two semi-circles each of radius 2 cm, with centres M and N respectively.
3.
The locus of P is two straight lines that are d cm from L and parallel to it.
(b)
Level 2
The locus of E is a circle with centre C and radius
EC .
7.
4.
The locus of P is a circle with centre O and radius OP .
8.
The locus of P is made up of three line segments, one at a distance of 1 cm from the horizontal line and two at a distance of 1 cm from the other, with three semi-circles each of radius 1 cm, with the vertices as the centres respectively.
5.
The locus of P is the angle bisector of

CAB .
9.
The locus of P is two circles, each with the same centre as the circle with radius 2 cm and radii 1 cm and 3 cm respectively.
The locus of P is a circle with the same centre as the circle with radius 1 cm and the radius of P is 2.5 cm.
6. (a)
The locus of P is made up of two parts.
Part one is made up of two pairs of parallel line segments, each at a distance of 1 cm from the square, with four quarters of a circle, each of radius 1 cm, centred at A , B , C and D respectively. Part two is a square with size 1 cm ×
1 cm which lies at the centre of ABCD .
2 radius AC .
The locus of vertex A is a circle with centre C and

11 Qualitative Treatment of Locus
13.
10.
The locus of P is the angle bisectors of the angles between
L
1
and L
2
.
11. (a)
The locus of P is an arc of the circle passing through points A , B and P .
14. (a) The locus of P is the straight line which bisects AB and perpendicular to AB as shown:
(b) The locus of Q is the circle with the mid-point O of
AC as the centre as shown:
For a fixed circle with centre O such as the middle one shown above, the locus of P are circles lying inside or outside the fixed circle which touch A .
(b)
(c) The possible locations of a point M are the intersections of the loci of P and Q as shown:
12.
The locus of P is a circle with centre O and radius
6 cm.
15.
The locus of the snail in the first 18 s is the curve as shown:
The locus of P is two straight lines that are 4 cm from AB and parallel to it.
3

Certificate Mathematics in Action Full Solutions 5A
Revision Exercise 11 (p. 19)
Level 1
1.
3.
The locus of P is made up of two pairs of parallel line segments, each at a distance of 1 cm from the rhombus, with four quarters of a circle, each of radius 1 cm, centred at A , B , C and D respectively.
2. (a)
The locus of P is made up of two pairs of parallel line segments, each at a distance of 1 cm from one of the line segments, with two semi-circles each of radius 1 cm, with the vertices as the centres respectively, and a quarter circle of radius 1 cm centred at the intersection point of the two line segments.
4.
The locus of P is the straight line passing through the mid-points of AD and BC as shown.
(b)
5.
The locus of P is the straight line that joins A and P as shown.
The locus of P is the straight line AC .
(c)
The locus of P is the straight line that passes through C and is perpendicular to AB .
Level 2
6.
The locus of P is the straight line passing through B and D .
4
The locus of P is the curve as shown.

7.
11. (a)
11 Qualitative Treatment of Locus
The locus of P is the curve as shown.
8.
The locus of P is a circle with diameter AB .
(b)
The locus of P is the curve composed of two arcs of
9. circles of radii 3 cm and 4 cm respectively as shown.
The locus of P is a larger circle with the same centre as the fixed circle as shown.
10.
The locus of
MN
P
as a chord.
is made up of two arcs of two circles with
The locus of Q is the arc of the circle passing through
A , B and Q .
12. (a) The locus of P is a circle with radius the same as that of the fixed circle.
(b) The locus of Q is a circle with radius the same as that of the fixed circle.
(c) no
13.
The locus of P is a circle such that its tangents passing through F and the tangents of the fixed circle passing through F are common.
5

Certificate Mathematics in Action Full Solutions 5A
14.
The locus of P is the curve as shown.
Multiple Choice Questions (p. 22)
1.
Answer: B
2.
Answer: A
3.
Answer: C
4.
Answer: A
5.
Answer: D
6.
Answer: D
7.
Answer: B
8.
Answer: B
6