5ach11(qualitative Treatment Of Locus)

11 Qualitative Treatment of Locus

11 Qualitative Treatment of Locus • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • each of radius 1 cm, with centres X and Y respectively.

Activity Activity 11.1 (p. 3)

3.

1.

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.

(a)

p. 16 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.

(b) 4.

(a) The locus of P is a smaller circle which lies inside the given circle. (b) no

5.

2.

(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.

(a)

(c) no (b)

Exercise Follow-up Exercise

Exercise 11A (p. 9)

p. 9

Level 1

1. The locus of P is a circle with centre O and radius 2 cm.

1. 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.

2. 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

1

Mathematics in Action Full Solutions 1A

(b) 2. The locus of E is a circle with centre C and radius EC.

The locus of P is two straight lines that are d cm from L and parallel to it.

Level 2

3. The locus of P is a circle with centre O and radius OP.

7. 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.

4. The locus of P is the angle bisector of ∠CAB.

8. 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.

5. 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.

9.

(a) The locus of vertex A is a circle with centre C and radius AC.

2

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

11 Qualitative Treatment of Locus

cm which lies at the centre of ABCD.

The locus of P is two straight lines that are 4 cm from AB and parallel to it.

13. The locus of P is an arc of the circle passing through points A, B and P.

10. The locus of P is the angle bisectors of the angles between L1 and L2.

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:

11. (a) 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.

(c) The possible locations of a point M are the intersections of the loci of P and Q as shown:

(b) 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:

12.

3

Mathematics in Action Full Solutions 1A

(c) The locus of P is the straight line passing through B and D.

Revision Exercise 11 (p. 19) Level 1

3. 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.

1. 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.

4. 2.

(a)

The locus of P is the straight line that joins A and P as shown. The locus of P is the straight line passing through the mid-points of AD and BC as shown.

(b) The locus of P is the straight line AC.

4

5.

11 Qualitative Treatment of Locus

The locus of P is the straight line that passes through C and is perpendicular to AB.

Level 2

6. 9. The locus of P is the curve as shown.

The locus of P is a larger circle with the same centre as the fixed circle as shown.

10. The locus of P is made up of two arcs of two circles with MN as a chord. 7. The locus of P is the curve as shown.

11. (a) The locus of P is a circle with diameter AB.

8. The locus of P is the curve composed of two arcs of circles of radii 3 cm and 4 cm respectively as shown.

(b) The locus of Q is the arc of the circle passing through A, B and Q.

5

Mathematics in Action Full Solutions 1A

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. 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

6.

Answer: D

7.

Answer: B

8.

Answer: B