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WorksheetsF3 LOCI IN TWO DIMENSION 2.0
Total questions: 20
Worksheet time: 15mins
A moving point P maintains an equal distance from two parallel lines. Which of the following does the locus of P belong to?
A circle
A straight line
Two parallel lines
Two perpendicular lines
The figure shows an equilateral triangle ABC. Which of the following lines may represent the locus of a point P such that AP = PB?
None of the above
Let A and B be two points. P is a point such that PA = PB, what is the locus of P?
The locus of P is a circle with diameter AB
The locus of P is circle with centre A and radius AB
The locus of P is the perpendicular bisector of AB
The locus of P is a pair of lines parallel to AB.
What is the definition of a locus of points?
The sum of two numbers
The product of two numbers
A set of points that satisfy a certain condition or property
The square root of a number
The set of points (locus) at a given distance from a straight line is _______.
a circle
one straight line
two intersecting lines
two parallel lines
The set of points (locus) equidistant from two fixed points is ______.
one circle
one straight line
two circles
two straight lines
Which construction is shown here?
Perpendicular bisector
Angle bisector
ASA triangle
SAS triangle
Which construction is shown here?
Perpendicular bisector
Angle bisector
Line bisector
Perpendicular
What shape would be produced by all the points which are 20cm away from a point?
Circle
Discorectangle (rectangle with semicircles on the end)
Straight line
Arc
What shape would be produced by all the points which are equidistant from two points A and B?
Circle
Discorectangle (rectangle with semicircles on the end)
Straight line
Arc
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
B
C
D
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?
L and Q
N and S
M and R
K and P
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
N
P
M
L
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?
L and G
L and J
G and J
L, G and J
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?
S and T
Q and R
R and T
P and T
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
S and T only
T and V only
S and V only
U and V only
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
B
C
D
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
B
C
D
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?
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
AE
AC
BE
BD
