The document contains 17 multi-part questions about loci and constructing loci. It asks the reader to describe, construct, and find intersections of loci in situations involving points moving in relation to lines, circles, polygons, and axes. Diagrams with points and geometric shapes are provided, and the reader is asked to draw loci on the diagrams and mark their intersections.

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LOCI
1. Describe the locus of point W in each of the following situations.
a A point W moves in a way that is always 4 cm
from point X.
b A point X moves in a way that it is always
equidistant from points N and O.
c A point Y moves in a way that always 6 cm from
a straight line PQ.
d A point Z moves in a way that is always
equidistant from two intersecting lines PQ and
RS.
X N O
Q
P
R
S
P
Q

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2. Construct the locus of point T in each of the following situations.
a A point T moves in such a way that it is always
equidistant from K and L.
b A point U moves in a way that is always 3 cm
from point V.
c A point V moves in a way that is always
equidistant from the straight lines AB and AC.
d A point K moves in a way that is always 2 cm
from the straight line MN.
K
L
V
M
N
A
B
C

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3. Diagram 3 shows KLOP and LMNO are squares with sides of 5 cm each. PLN is a semicircle with center
O. X is a point which moves in such a way that its distance from O is always 5 cm, Y is a point which
moves in such a way that perpendicular distance from line KLM is always 5 cm.
Diagram 3
Which of the points are intersections of locus X and locus Y?
N
O
K
P
L M

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4. Diagram 4 shows two semicircles of radius 3 cm and 5 cm.
Diagram 4
Locate the points which are both 3 cm from T and 5 cm from S?
5. Diagram 5 shows a circle of radius 5 cm. XY is a perpendicular bisector of line OE.
Diagram 5
X
Z
Y
S
5 cm
T
3 cm
W
X
Y
E
C
B
A
O
V

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Which of the points A, B, C and D is equidistant from O and E and 5 cm from O?
6. Diagram 6 shows a square RSTU which is 6 cm. X, Y and Z are three points moving in the diagram.
a. X is moving in the diagram such that it is equidistant from the line ST and line TU. By using the
letters in the diagram, state the locus of X.
b. On the diagram:
i. Construct locus Y such that TY = 5 cm.
ii. Construct locus Z such that RZ = ZT
c. Mark with  all the possible points of intersection between locus Y and locus Z.
Answer / Jawapan:
a.
b / c.
Diagram 6
R
U
S
T

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7. Diagram 7 in the answer space shows a square RSTU drawn on a grid of equal squares with sides of 1
unit.
On the diagram:
a. Construct the locus of point F moving at a distance of 4 units from K.
b. Construct the locus of a moving point E which is equidistant from the point M and N.
c. Mark with the symbol  for all the intersections that satisfy the loci in ( a ) and ( b ).
M
N K
Diagram 7
R S
T
U

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8. Diagram 8 shows two congruent squares, PQTU and QRST. X and Y are two moving points on the diagram.
a. On the diagram, draw:
i. the locus X such that its distance from straight line QT is 2 cm.
ii. the locus of Y such that YT = QT.
b. Hence,mark with the symbol  the intersection of locus X and locus Y.
Diagram 8
9. Diagram 9 in the answer space shows a square PQRS drawn on a square grid of equal squares with sides of
1 unit. M and N are two moving points in the diagram.
a. On the diagram, draw:
i. the locus M such that is constantly 5 units from point P.
ii. the locus for the point N that is equidistant from PQ and PS.
b. Hence,mark with the symbol  the intersection of locus M and locus N.
Diagram 9
R
Q
U
P
T S
R
Q
P
S

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10. Diagram 10 in the answer space shows a regular pentagon PQRST. A, B, C, D and E are the midpoint of
PQ, QR, RS,ST and PT respectively. W, X and Y are three moving point in the diagram.
Rajah 10 di ruang jawapan menunjukkan sebuah pentagon sekata PQRST. A, B, C, D dan E ialah masing-
masing titik tengah bagi PQ, QR, RS, ST dan PT. W, X dan Y adalah tiga titik yang bergerak dalam rajah
itu.
(a) W is a point which moves such that it is equidistant from PT and PQ
By using the letters in Diagram 10, state the locus of W.
W ialah satu titik yang bergerak dengan keadaan jaraknya adalah sama dari PT dan PQ.
Dengan menggunakan huruf di dalamRajah 10, nyatakan lokus bagi W.
(b) On Diagram 10, draw:
Pada Rajah 10, lukis:
(i) the locus of X such that XR = RS,
lokus bagi X dengan keadaan XR = RS,
(ii) the locus of Y such that its equidistant from point P and point S.
lokus bagi Y dengan keadaan jaraknya sentiasa sama dari titik P dan titik S.
(c) Hence,mark with the symbol  the intersection of the loci of X and the loci of Y.
Seterusnya, tandakan dengan simbol  titik persilangan lokus X dan lokus Y.
[5 marks / markah]
Answer / Jawapan:
(a)
(b),(i), (ii)
(c)
Diagram 10 / Rajah 10
P
R
C
Q
B
A
D
E
T
S

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11. Diagram 11 in the answer space drawn on a grid of equal squares with sides of 1 unit. X, Y and Z are three
moving points in the diagram.
Rajah 11 di ruang jawapan dilukis pada grid segiempat sama bersisi 1 unit. X, Y dan Z adalah tiga titik
yang bergerak di dalamrajah itu.
(a) X moves such that it is equidistant from point J and point L. By using the letters in the diagram, state
the locus of X.
X bergerak dengan jarak dari titik J dan L adalah sentiasa sama. Dengan menggunakan huruf abjad
pada rajah itu, nyatakan lokus bagi X
(b) On the diagram, draw :
Pada rajah, lukis :
(i) the locus of Y such that its distance from M is 6 unit.
lokus bagi Y dengan keadaan 6 unit dari M.
(ii) the locus of Z such that is constantly 1 unit from the line PQ.
lokus Z dengan keadaan jarak tegak Z dari garis PQ ialah 1 unit.
(c) Hence,mark with the symbol  for all the intersection of the locus of Y and locus of Z.
Seterusnya, tandakan dengan symbol  kedudukan bagi persilangan lokus Y dan lokus Z.
[5 marks]
Answer/ Jawapan :
(a)
Diagram 11 / Rajah 11
J K
L
M
P
Q
P

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12. Diagram 12 in the answer space shows a circle with center O, drawn on a grid of equal squares with sides
of 1 unit. AOB is a diameter of the circle.
X, Y and Z are three moving points in the circle.
Rajah 12 di ruang jawapan menunjukkan sebuah bulatan berpusat O yang dilukis pada grid segiempat
sama bersisi 1 unit. AOB ialah diameter bulatan itu.
X, Y dan Z adalah tiga titik yang bergerak di dalam bulatan itu.
(a) X is the point which moves such that it is constantly 3 units from the point O. Describe fully the locus
of X.
X titik yang bergerak dengan dengan keadaan titik itu sentiasa berjarak 3 unit dari O. Huraikan
selengkapnya lokus bagi X
(b) On Diagram 10, draw :
Pada rajah 10, lukis :
(i) the locus of the point Y which moves such that its distance is constantly 2 units from the line
AB.
lokus bagi titik Y yang bergerak dengan keadaan titik itu sentiasa berjarak 2 unit dari garis
AB.
(ii) the locus of the point Z which moves such that it is equidistant from the the point A and the
point B.
lokus bagi titik Z yang bergerak dengan keadaan jaraknya adalah sama dari titik A dan titik B.
(c) Hence,mark with the symbol  for all the intersections of the locus of Y and the locus of Z.
Seterusnya, tandakan dengan symbol  kedudukan bagi semua persilangan lokus Y dan lokus Z.
Answer / Jawapan : [5 marks]
(a)
A B
O

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Diagram 12 / Rajah 12
13. Diagram 13 in the answer space shows a regular hexagon ABCDEF. Y and Z are two moving points in
the hexagon.
Rajah 13 di ruang jawapan menunjukkan sebuah heksagon sekata ABCDEF. Y dan Z adalah dua titik
yang bergerak di dalamheksagon itu.
On Diagram 13, draw :
Pada Rajah 13, lukis :
(i) the locus of Y such that YD = DE.
lokus bagi Y dengan keadaan YD = DE.
(ii) the locus of Z such that it is equidistant from point B and point F.
lokus bagi Z dengan keadaan Z sentiasa berjarak sama dari titik B dan titik F.
(iii) hence, mark with the symbol  the intersections of the locus of Y and the locus of Z.
seterusnya,tandakan dengan symbol  kedudukan bagi persilangan lokus Y dan lokus Z itu.
[3 marks]
Answer :
Diagram 13 / Rajah 13
C
B
A
D
F
E

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14. Diagram 14 in the answer space shows an isosceles triangle PQR drawn on grid of equal squares with sides
of 1 unit. X and Y are two moving points inside the triangle PQR.
Rajah 14 di ruang jawapan menunjukkan sebuah segi tiga sama kaki PQR yang dilukis pada grid segi
empat sama bersisi 1 unit. X dan Y adalah dua titik yang bergerak di dalamsegi tiga PQR.
(a) On Diagram 13, draw :
Pada Rajah 13, lukis :
(i) the locus of the point X which moves such that its distance is constantly 6 units from the point
Q.
lokus bagi titik X yang bergerak dengan keadaan titik itu sentiasa berjarak 6 unit dari titik Q.
(ii) the locus of the point Y which moves such that its distance is constantly 3 units from the line
PQ.
lokus bagi titik Y yang bergerak dengan keadaan titik itu sentiasa berjarak 3 unit dari garis
PQ.
(b) Hence,mark with the symbol  the intersections of the locus of X and the locus of Y.
Seterusnya, tandakan dengan symbol  kedudukan bagi persilangan lokus X dan lokus Y itu.
[3 marks]
Answer :
(a)
(b)
R
P Q

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Diagram 14 / Rajah 14
15. Diagram 15 in the answer space shows a semicircle with centre O, drawn on a grid of equal squares with
sides of 1 unit. POQ is the diameter of the semicircle. Y and Z are two moving points inside the diagram.
Rajah 15 di ruang jawapan menunjukkan sebuah semibulatan berpusat O, dilukis pada grid segi empat
sama bersisi 1 unit. POQ ialah diameter bagi semibulatan itu. Y dan Z adalah dua titik bergerak di dalam
rajah itu.
( a ) On the diagram 15, draw
Pada rajah 15, lukis
(i) the locus of point Y which moves such that its distance is constantly 3 unit from the line PQ.
lokus bagi titik Y yang bergerak dengan keadaan titik itu sentiasa berjarak 3 unit dari garis
PQ.
(ii) the locus of point Z which moves such that it is equidistant from point P and point Q.
lokus bagi titik Z yang bergerak dengan keadaan jaraknya adalah sentiasa sama dari titik P
dan titik Q.
(b) Hence,mark with the symbol  the intersection of the locus Y and the locus Z.
Seterusnya, tandakan dengan simbol  kedudukan bagi semua persilangan lokusY dan LokusZ itu.
[ 4 marks ]
Answer / Jawapan:
(a)/ (b)
P O Q
Diagram 15 / Rajah 15

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16. Diagram 16 in the answer space shows triangle ABC.
X and Y are two moving points in the diagram.
Rajah 16 di ruang jawapan menunjukkan sebuah segitiga ABC.
X dan Y adalah dua titik yang bergerak di dalamrajah itu.
On Diagram 16, draw
Pada rajah 16, lukis
(i) the locus of X such that it is always equidistant from the lines AB and AC.
lokus bagi X dengan keadaan jarak tegaknya sentiasa sama dari garis AB dan AC.
(ii) the locus of Y such that YC = 3 cm
lokus bagi Y dengan keadaan YC = 3cm
(iii) Hence,mark with the symbol the intersection of the locus of X and the locus of Y.
Seterusnya, tandakan dengan  kedudukan bagi persilangan lokus X dan lokus Y itu.
[ 3 marks ]
Answer / Jawapan :
Diagram 16 / Rajah 16
C A
B

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17. Diagram 17 in the answer space shows the x-axis and y-axis drawn on a grid of sides 1 unit. P and Q are
two moving points in the diagram.
Rajah 17 di ruang jawapan menunjukkan paksi-x dan paksi-y yang dilukis pada grid segiempat sama
bersisi 1 unit. P dan Q bergerak dalamrajah itu.
(a) On Diagram 7, draw
Pada Rajah 7, lukis
(i) the locus of P which is moving at fixed distance of 5 unit from (6 , 6).
lokus P yang bergerak dengan keadaan jarak tetap 5 unit dari (6 , 6).
(ii) the locus of Q which is moving equidistant from x -axis and y -axis.
lokus Q yang bergerak dengan keadaan sama jarak dari paksi-x dan paksi-y.
(b) Hence,mark with the symbol  the intersection of the locus P and locus Q.
Seterusnya, tandakan dengan simbol  kedudukan bagi persilangan lokus P dan Q itu.
[5 marks ]
Answer / Jawapan:
(a) / (b)(i),(ii),
Diagram 17 / Rajah 17
2 4 6 8 10
0
2
4
6
8
10

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18. Diagram 18 in the answer space shows a square KLMN. P and Q are two moving points in the diagram.
Rajah 18 di ruang jawapan menunjukkan sebuah segiempat sama KLMN. P dan Q adalah dua titik yang
bergerak dalamrajah itu.
On the diagram:
Pada rajah :
(a) construct the locus of point P such that it is constantly 4 units from M
bina lokus bagi titik P dengan keadaan sentiasa berjarak tetap 4 unit dari M
(b) construct the locus of the point Q such that KL = KN
bina lokus bagi titik Q dengan keadaan KL = KN.
(c) hence, mark with the symbol , the intersections of the locus of P and the locus of Q
seterusnya, gtandakan dengan simbol,persilangan bagi lokus P dan lokus Q
[ 4 marks ]
K L
M
N

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19 Diagram 19 in the answer space shows a square ABCD. P,Q, R and S are the midpoints of AB, BC, CD
and AD respectively.
Rajah 19 di ruang jawapan menunjukkan sebuah segi empat sama ABCD. P, Q, R dan S adalah
masing-masing titik tengah bagi AB, BC, CD dan AD.
X, Y, and Z are the three points that move in the diagram.
X, Y dan Z adalah tiga titik yang bergerak di dalamrajah.
(a) X is the point which moves such that it is equidistant from the straight lines AB and AD. By
using the letters in the diagram, state the locus of X.
X ialah titik yang bergerak dengan keadaan sentiasa sama jarak dari garis lurus AB dan AD.
Dengan menggunakan huruf pada rajah, nyatakan lokus bagi X.
(b) On the diagram, draw :
Pada rajah, lukis:
(i) the locus of point Y, such that OY = OP.
lokus bagi titik Y, dengan keadaan OY = OP.
(ii) the locus of point Z that is constantly 2 cm from the line SQ.
lokus bagi titik Z yang berjarak tetap 2 cmdari garis SQ.
( c) State the number of intersection of the locus of Y and the locus of Z.
Nyatakan bilangan persilangan bagi lokusY dan lokusZ
[5 marks]
Answer / Jawapan:
(a)
(b)
Diagram 19 / Rajah 19
(c)
A B
C
D
O
P
R
Q
S