Chapter 8 Loci in 2 Dimensions (8.2 Quiz)

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