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Chapter 8 Loci in 2 Dimensions (8.2 Quiz)

Total questions: 15

Worksheet time: 8mins

Name
Class
Date
1.

In the diagram, PQRS is a square. PTR is an arc of a circle with centre S. QUS is an arc of a circle with centre P.


X is the locus of a point which moves such that its distance from S is always constant. Y is the locus of a point which moves such that it is equidistant from the lines PQ and QR. Which of the points, A, B, C or D, is the intersection of the locus X and the locus Y?

a)

A

b)

B

c)

C

d)

D

2.

The diagram shows a circle with centre O and a radius of 5 cm. The circle is divided into 8 equal parts.


Which two points are intersections of two loci which are always 5 cm from point O and 5 cm from the line LOQ?

a)

L and Q

b)

N and S

c)

M and R

d)

K and P

3.

In the diagram, P is the common centre of two circles, KRUQM and LTN, while Q is the common centre of the circles KLPUS and MNT.


A point Y moves such that it is always equidistant from points R and S.

The locus of Y is

a)

the arc KM.

b)

the straight line KU.

c)

the arc LN.

d)

the straight line LM.

4.

In the diagram, PQR is an equilateral triangle with sides of 4 cm. UM and KL are two circular arcs with Q as the centre. K is the midpoint of UP.


X is the locus of a point which moves such that its distance from Q is always 3 cm. Y is the locus of a point which moves such that YQ = YR. The point of intersection of the locus X and locus Y is

a)

N

b)

P

c)

M

d)

L

5.

In the diagram, FGKL and GHJK are squares each with sides of 3 cm. LGJ is a semicircle with centre K.


X is a point which moves such that its distance from K is always 3 cm.

Y is a point which moves such that its perpendicular distance from line FGH is always 3 cm.

Which of the following are the intersection points of loci of X and Y?

a)

L and G

b)

L and J

c)

G and J

d)

L, G and J

6.

A point moves such that it is always 5 cm from a fixed point O. Which of the dotted lines below shows the locus of the point?

a)

A

b)

B

c)

C

d)

D

7.

The diagram shows two circles with centres O and P. Given OP = 4 cm, S is the midpoint of OP and Q is the midpoint of SP.


A point L moves such that it is always 3 cm from point O. A point M moves such that it is always 2 cm from point P.

Which of the following points are the intersection of locus L and locus M?

a)

S and T

b)

Q and R

c)

R and T

d)

P and T

8.

The diagram shows two squares PQTU and QRST of the same size. UQS is a semicircle with centre T and PQR is a straight line. X is the locus of a point which moves such that its distance from Q is always constant. Y is the locus of a point which moves such that its perpendicular distance from line UTS is always constant.


Which of the following are points of intersection of locus X and locus Y?

a)

T and R

b)

P and T

c)

P and R

d)

U and S

9.

The diagram shows a Cartesian plane.


A point P moves on the plane such that it is always 3 units from the y-axis.

Another point Q moves such that it is always 3 units from point M.

The points of intersection of the loci of P and Q are

a)

S and T only

b)

T and V only

c)

S and V only

d)

U and V only

10.

In the diagram, X and Y are the centres of two circles.


Which of the points, P, Q, R or S, is equidistant from X and Y ?

a)

P only

b)

Q only

c)

P and R only

d)

R and S only

11.

In the diagram, MN and RS are two circular arcs with a common centre O and with radii 4 cm and 8 cm respectively.


OT is the bisector of ∠ROS. A point P moves such that it is more than 4 cm but less than 8 cm from point O, and is always equidistant from lines OR and OS.

Which of the points, A, B, C or D, is a possible position of point P ?

a)

A

b)

B

c)

C

d)

D

12.

In the diagram, P and Q are centres of two circles.


Which of the points, A, B, C or D, is 5 cm from P and less than 3 cm from Q?

a)

A

b)

B

c)

C

d)

D

13.

The diagram shows a fan where the points M, N, P and R are equidistance from point O.


When the fan is switched on, part of the locus of point P is

a)

the straight line OP.

b)

the straight line NP.

c)

the arc PR with centre O.

d)

the arc NP with centre O.

14.

A point moves such that it is equidistant from two fixed points, H and K.

The locus of the moving point is

a)

an arc that joins points H and K.

b)

a perpendicular bisector of the straight line that joins points H and K.

c)

a circle that passes through points H and K.

d)

a line that is parallel to the line joining points H and K.

15.

What is the locus of a coconut falling from a tree?

a)

A vertical line

b)

A horizontal line

c)

A parabola

d)

A circle