Rectangular Coordinate System (I) 8.53
13. The figure shows 3DEF with vertices D(2 , 3), E(1 , 1) and
F(5 , 1). D, E and F are translated downwards by 3 units to Dl, El
and Fl respectively.
(a) Find the coordinates of Dl, El and Fl.
(b) Draw 3DlElFl in the figure.
14. The figure shows 3PQR with vertices P(-3 , 3), Q(-1 , 2) and
R(-1 , -1). P, Q and R are reflected in the y-axis to points Pl, Ql
and Rl respectively.
(a) Find the coordinates of Pl, Ql and Rl.
(b) Draw 3PlQlRl in the figure.
15. The figure shows 3STU with vertices S(-1 , 2), T(-3 , -1) and
U(-1 , -2). S, T and U are rotated about the origin O through 180c
to Sl, Tl and Ul respectively.
(a) Find the coordinates of Sl, Tl and Ul.
(b) Draw 3SlTlUl in the figure.
16. Refer to the figure.
(a) Write down the coordinates of A and B.
(b) A and B are translated 5 units downwards to Al and Bl
respectively.
(i) Find the coordinates of Al and Bl.
(ii) Is AlBl a horizontal line? Explain your answer.
17. Refer to the figure.
(a) Write down the coordinates of C and D.
(b) C and D are reflected in the y-axis to Cl and Dl respectively.
(i) Find the coordinates of Cl and Dl.
(ii) Is ClDl a vertical line? Explain your answer.
18. Refer to the figure.
(a) Write down the coordinates of E and F.
(b) E and F are rotated anticlockwise about the origin O through
90c to El and Fl respectively.
(i) Find the coordinates of El and Fl.
(ii) Is ElFl a horizontal line? Explain your answer.
y
x
-1
1
2
3
-2
3 4 5
21
D
E F
0
➥ Example 14
y
x
-1
1
2
3
3 4
-1-2-3 210
P
Q
R
➥ Example 15
y
x
-1
1
2
3
3
-1-2-3 2
-2
-3
1
T
O
S
U
y
x
-1
1
2
-1-2-3-4-5 21
B
A
0
Explain
y
x
-1
1
2
3 4
-1-2-3-4 2
-2
10
D
C
Explain
y
x
-1
1
2
3
-1-2-3 2
3
-2
-3
1O
E
F
Explain
1
1
2
2
3
3
Dl(2 , 0), El(1 , -2), Fl(5 , -2)
Pl(3 , 3), Ql(1 , 2), Rl(1 , -1)
Sl(1 , -2), Tl(3 , 1), Ul(1 , 2)
A(-5 , 2), B(-1 , 2)
Al(-5 , -3), Bl(-1 , -3)
Cl(4 , 1), Dl(4 , -2)
El(2 , -2), Fl(2 , 3)
no
yes
C(-4 , 1), D(-4 , -2)
E(-2 , -2), F(3 , -2)
yes
D'
E' F'
P'
R'
Q'
T'
U'
S'