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Worksheets

Locus in 2 Dimension

Total questions: 20

Worksheet time: 12mins

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.

Which construction is shown here?

a)

Perpendicular bisector

b)

Angle bisector

c)

ASA triangle

d)

SAS triangle

4.

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

5.

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)
6.

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

7.

The locus of all the points at a fixed distance and less from a point A can be shown as a

a)

circumference

b)

circle

c)

square

d)

straight line

8.

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.

9.

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

10.

Which construction is shown here?

a)

Perpendicular bisector

b)

Angle bisector

c)

ASA triangle

d)

SAS triangle

11.

Which construction is shown here?

a)

Perpendicular bisector

b)

Angle bisector

c)

Line bisector

d)

Perpendicular

12.

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

13.

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

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