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F3 LOCI IN TWO DIMENSION 2.0

Total questions: 20

Worksheet time: 15mins

Name
Class
Date
1.

A moving point P maintains an equal distance from two parallel lines. Which of the following does the locus of P belong to?

a)

A circle

b)

A straight line

c)

Two parallel lines

d)

Two perpendicular lines

2.

The figure shows an equilateral triangle ABC. Which of the following lines may represent the locus of a point P such that AP = PB?

a)
b)
c)
d)

None of the above

3.

Let A and B be two points. P is a point such that PA = PB, what is the locus of P?

a)

The locus of P is a circle with diameter AB

b)

The locus of P is circle with centre A and radius AB

c)

The locus of P is the perpendicular bisector of AB

d)

The locus of P is a pair of lines parallel to AB.

4.

What is the definition of a locus of points?

a)

The sum of two numbers

b)

The product of two numbers

c)

A set of points that satisfy a certain condition or property

d)

The square root of a number

5.

The set of points (locus) at a given distance from a straight line is _______.

a)

a circle

b)

one straight line

c)

two intersecting lines

d)

two parallel lines

6.

The set of points (locus) equidistant from two fixed points is ______.

a)

one circle

b)

one straight line

c)

two circles

d)

two straight lines

7.

Which construction is shown here?

a)

Perpendicular bisector

b)

Angle bisector

c)

ASA triangle

d)

SAS triangle

8.

Which construction is shown here?

a)

Perpendicular bisector

b)

Angle bisector

c)

Line bisector

d)

Perpendicular

9.

What shape would be produced by all the points which are 20cm away from a point?

a)

Circle

b)

Discorectangle (rectangle with semicircles on the end)

c)

Straight line

d)

Arc

10.

What shape would be produced by all the points which are equidistant from two points A and B?

a)

Circle

b)

Discorectangle (rectangle with semicircles on the end)

c)

Straight line

d)

Arc

11.

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

12.

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

13.

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

14.

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

15.

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

16.

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

17.

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

18.

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

19.

Given a line segment AB of length 4 cm, which of the following dotted lines may represent the locus of a point P such that the area of △PAB is always equal to 4 cm2?

a)
b)
c)
d)
20.

In the figure, ABCD is a square and its diagonals intersect at E. P is a moving point inside or on the square such that P is equidistant from AB and AD. The locus of P is

a)

AE

b)

AC

c)

BE

d)

BD