Compound Compound LocusLocus

Compound Compound LocusLocus

Page 7-9Page 7-9

Compound Locus Examples:

Ex 1: Identify the points 4 units away from line AB and 6 units away from a point on line AB.

4

4

6

For each of the following examples, sketch the compound Loci.

A B

Compound Locus Examples:Ex 2: Identify the points equidistant from 2 intersecting lines and 5 units from the point of intersection.

5

2

2

2

b

a

Compound Locus Examples:Ex 3: Identify the points equidistant from 2 parallel lines a and b that are 4 units apart and 2 units from a point on line b.

1. What is the number of points in a plane at a given distance from a given line and also equidistant from two points on the given line?

d

d

2. How many points are there in a plane that are 4 cm from a given line and also 5 cm from a given point on that line?

4 cm

4 cm

5 cm

3. How many points are there in a plane that are 5 cm from a given line and also 5 cm from a given point on that line?

5 cm

5 cm

5 cm

4. Two points A and B are 6” apart. How many points are there that are equidistant from both A and B and also 5 inches from A?

3“

5“

B A

3“

5. How many points are there that are equidistant from two given points A and B and also 2 inches from the line passing through A and B?

2”

2”

A B

6. LM and RS are two parallel lines 10 mm apart, and A is a point on LM. How many points are there that are equidistant from LM and RS and 7 mm from A?

5 mm

5 mm

7 mm

L M

R S

A

7. Two lines AB and CD, intersect at E. How many points are 2 units from E and also equidistant from AB and CD?

AB

C

D

E

2

8. A point P is 1 unit from a line, AB. How many points in the plane are 2 units from AB and also 4 units from P?

2

2

4

A B

P1

House

18 m

8 m

B

A

10. The treasure is 6 m from A and 12 m from B.

612

House

18 m

8 m

B

A

11. The treasure is 10m north of the house and 3m from A.

3 m10 m

House

18 m

8 m

B

A

10

15

12. The treasure is 10 m from A and 15 m from B.

7”

A B

16. Two points A and B are 7 inches apart. How many points are there that are 12 inches from A and also 4 inches from B.

12”

4”

18.The number of points that are at a given distance from a given line and also equidistant from two given points on the line is

(1) 1 (2) 2 (3) 3 (4) 4

d

d

19. The number of points in a plane 1 cm from a given line and 2 cm from a given point on the line is

(1) 1 (2) 2 (3) 0 (4) 4

1 cm

1 cm

2 cm

20. The number of points in a plane 2 cm from a given line and 1 cm from a given point on the line is

(1) 1 (2) 2 (3) 0 (4) 4

2 cm

2 cm

1 cm

3

C

21. Point C is 2 units from a line, AB. How many points in AB are three units from point C.

(1) 1 (2) 2 (3) 0 (4) 4

2A B

22. AB is 1 cm long. How many points in the plane are 2 cm from both A and B?

(1) 1 (2) 2 (3) 0 (4) 4

2 cm

A B

2 cm

1 cm

23.Parallel lines k and t are 6 mm apart, and A is a point on line t. The number of points equidistant from k and t and also 3 mm from A is?

(1) 1 (2) 2 (3) 0 (4) 4

3 mm

3 mm

3 mm

t

k

A

24. AB and CD are parallel and are 6” apart. Point P is on AB. The number of points equidistant from these two lines and also 5 “ from point P is?

(1) 1 (2) 2 (3) 0 (4) 4

3”

3”

5”

A B

C D

P

10

25. Point P is 7 units from a given line. The number of points that are 3 units from the line and also 10 units from point P is

(1) 1 (2) 2 (3) 3 (4) 4

7

P

3

3

27. Write an equation of the locus of points equidistant from (0,-3) and (0,7).

2y

28.a) Draw the locus of points equidistant from the points (4,1) and (4,5) and write an equation for the locus.

b) Draw the locus of points equidistant from the points (3,2) and (9,2) and write an equation for the locus.

c) Find the number of points that satisfy both conditions stated in a and b. Give the coordinates for each point found.

3y

6x

)3,6(

29.a) Represent graphically the locus of points (1) 3 units from the line x=1 (2) 4 units from the line y=-2

b) Write the equation for the loci represented in a.

c) Find the coordinates of the points of intersection of these loci.2x

2y)2,2(

4x

6y

)2,4()6,4( )6,2(

30. a) Represent graphically the locus of points (1) 8 units from the y-axis (2) 10 units from the origin

b) Write the equation for the loci represented in a.

c) Find the coordinates of the points of intersection of these loci.8x

)6,8(

8x

)6,8()6,8( )6,8(

32. a) Draw the locus of points equidistantfrom the circles whose equations are and . Write an equation of the locus.

b) Draw the locus of points 4 units from the x-axis. Write an equation of the locus.

c) Find the coordinates of points that satisfy both conditions in a and b.

)4,0(

)4,0(

422 yx 3622 yx

16 ) 22 yxa

4y

4y

35. a) Write an equation of the locus of points 2 units from the x-axis.

b) Describe fully the locus of points at a distance d from P(2,6)

(1) d=2 (2) d=4 (3) d=6 (4) d=8 (5) d=10

2y

0 )1

2y

P

1 )22 )33 )44 )5