The document contains several examples of two-dimensional loci problems involving points moving within geometric shapes such as squares, triangles, circles, and hexagons. Each example provides diagrams showing the shapes and moving points, and poses questions about drawing the loci of the points and finding their intersections. The examples are intended to illustrate key concepts for representing and analyzing loci in two dimensions.

1. 17. Loci In Two Dimensions
PAPER 2
(2004,Q15)
Diagram 6 in the answer space shows four squares, PKJN, KQLJ, NJMS, JLRM.
W, X and Y are moving point’s in the diagram.
(a) W moves such that it is equidistant from the straight line PS and QR.
By using the letters in the diagram, state the locus of W.
(b) On the diagram, draw
(i) the locus of X such that XJ = JN
(ii) the locus of Y such that the distance from point Q and point S are the same.
(c) Hence, mark with the symbol ⊗all the intersections of the locus of X and the locus of Y.
[5 marks]
Answer:
(a)
(b)(c)
P Q
RS
K
J
M
N L
Diagram 6
(2005, Q9)
Diagram 6 in the answer space shows a square PQRS drawn on a grid of equal squares with size of 1 unit.
M, X and Y are three moving points in the diagram.
(a) M is the point which moves such that its distance from point Q and point S are the same.
By using the letters in the diagram, state the locus of M.
(b) On the diagram, draw
(i) the locus for the point X that is constantly 5 units from the line QR,
(ii) the locus for the point Y that is constantly 7 units from the points R.
(c) Hence, mark with the symbol ⊗the intersections of the locus of X and the locus of Y.
[5 marks]
Answer:
(a)
Khairunnasri Abdul Rashid 1

2. 17. Loci In Two Dimensions
(b)
P
Q R
S
Diagram 6
(2006, Q18)
Diagram 6 in the answer space shows a square PQRS drawn on a grid of equal squares with size of 1 unit.
W, X and Y are three moving points in the diagram.
(a) W is the point which moves such that its equidistant from the straight lines PQ and PS.
By using the letters in the diagram, state the locus of W.
(b) On the diagram, draw
(i) the locus for the point X that is constantly 5 units from the point P,
(ii) the locus for the point Y that is constantly 4 units from the straight line QR.
(c) Hence, mark with the symbol ⊗the intersections of the locus of X and the locus of Y.
[5 marks]
Answer:
P
S R
Q
Diagram 6
Khairunnasri Abdul Rashid 2

3. 17. Loci In Two Dimensions
(2007, Q16)
(a) Diagram 5 shows a rhombus MNOP.
X is a moving point in the rhombus such that
it is always equidistant from the straight lines
PM and PO.
By using the letters in the diagram,
state the locus of X.
(b) Diagram 6 in the answer space shows a regular hexagon ABCDEF.
Y and Z are two moving points in the hexagon.
On Diagram 6, draw
(i) the locus of Y such that YD = DE.
(ii) the locus of Z such that it is equidistant from point B and point F.
(c) Hence, mark with the symbol ⊗ the intersection of the locus of Y and the locus of Z.
[5marks]
Answer :
(a)
(b)(i),(ii)
(c)
(2008, Q10)
Diagram 10 in the answer space shows a circle with centre 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 inside the circle.
(a) X is the point which moves such that it is constantly 3 units from the point O.
Describe fully the locus of X.
(b) On Diagram 10, draw
(i) the locus of the point Y which moves such that its distance is constantly 2 units
from the line AB.
(ii) the locus of the point Y which moves such that it is equidistant from the point A
and the point B.
(c) Hence, mark with the symbol ⊗ the intersections of the locus of Y and the locus of Z.
[5marks]
Answer :
(a)
(b)(i),(ii)
(c)
Khairunnasri Abdul Rashid 3
Diagram 5
NM
P
O
Diagram 6
F
E D
C
BA

4. 17. Loci In Two Dimensions
(2009, Q10)
Diagram in the answer space shows an isosceles triangle PQR drawn on the grid of equal squares with sides of
1 unit. X and Y are two moving points inside the triange PQR.
a) On diagram, draw
i. The locus of point X which moves such that its distance is constantly 6 units from the point Q.
ii. The locus of point Y which moves such that its distance is constantly 3 units from the line PQ.
b) Hence, mark with the symbol ⊗ the intersection of the locus X and the locus Y.
(2010, Q16)
Khairunnasri Abdul Rashid 4
Diagram 10
O BA
R
QP

5. 17. Loci In Two Dimensions
Diagram in the answer space shows a square KLMN with sides of 6 units drawn on a grid of equal squares with
side 1 unit. X, Y and Z are three moving points inside the square.
Rajah di ruang jawapan menunjukkan sebuah segi empat sama KLMN dengan sisi 6 unit yang dilukis pada grid
segi empat sama bersisi 1 unit. X, Y dan Z adalah tiga titik yang bergerak di dalam segi empat sama itu.
a) X is the point which moves such that it is always equidistant from point K and point M.
By using the letters in diagram, state the locus of X.
X ialah titik yang bergerak dengan keadaan jaraknya adalah sentiasa sama dari titik K dan titik M.
Dengan menggunakan huruf di dalam rajah, nyatakan lokus bagi X.
b) On diagram, draw
Pada rajah, lukis
i) The locus of the point Y which moves such that it is always equidistant from the straight lines KL and KN,
Lokus bagi Y yang bergerak dengan keadaan jaraknya adalah sentiasa sama dari garis lurus KL dan KN,
ii) The locus of point Z which moves such that its distance is constantly 2 units from point P,
Lokus bagi titik Z yang bergerak dengan keadaan titik itu sentiasa berjarak 2 unit dari titik P,
c) Hence, mark with the symbol ⊗ 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 itu.
[5marks]
Answer :
(a)
(b)(i),(ii)
(c)
Khairunnasri Abdul Rashid 5
•
P
N M
LK

6. 17. Loci In Two Dimensions
Khairunnasri Abdul Rashid 6

7. 17. Loci In Two Dimensions
Khairunnasri Abdul Rashid 6