WorksheetsChapter 8 Loci in 2 Dimensions (8.2 Quiz)
Total questions: 15
Worksheet time: 8mins
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, 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
the arc KM.
the straight line KU.
the arc LN.
the straight line LM.
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
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
B
C
D
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 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?
T and R
P and T
P and R
U and S
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, X and Y are the centres of two circles.
Which of the points, P, Q, R or S, is equidistant from X and Y ?
P only
Q only
P and R only
R and S 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
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
the straight line OP.
the straight line NP.
the arc PR with centre O.
the arc NP with centre O.
A point moves such that it is equidistant from two fixed points, H and K.
The locus of the moving point is
an arc that joins points H and K.
a perpendicular bisector of the straight line that joins points H and K.
a circle that passes through points H and K.
a line that is parallel to the line joining points H and K.
What is the locus of a coconut falling from a tree?
A vertical line
A horizontal line
A parabola
A circle
