8.62 Chapter 8
Refer to the figure. Find the coordinates of the image formed
after a point P(-3 , -4) undergoes each of the following
transformations. [Nos. 16-18]
16. P is translated 5 units upwards and then translated 3 units
to the left.
17. P is reflected in the y-axis and then translated 2 units to
the right.
18. P is translated 1 unit downwards and then rotated clockwise
about the origin O through 90c.
19. The figure shows 3ABC with vertices A(3 , 2), B(2 , 3) and
C(1 , -1). A, B and C are translated to the left by 4 units to Al, Bl
and Cl respectively.
(a) Find the coordinates of Al, Bl and Cl.
(b) Draw 3AlBlCl in the figure.
20. The figure shows a parallelogram PQRS with vertices P(1 , 3),
Q(3 , 3), R(4 , 1) and S(2 , 1). P, Q, R and S are reflected in the
y-axis to Pl, Ql, Rl and Sl respectively.
(a) Find the coordinates of Pl, Ql, Rl and Sl.
(b) Draw PlQlRlSl in the figure.
21. The figure shows a line segment HK with end points H(-2 , 2) and
K(-1 , -1). H and K are rotated anticlockwise about the origin O
through 270c to Hl and Kl respectively.
(a) Find the coordinates of Hl and Kl.
(b) Draw HlKl in the figure.
In each of the following, find the coordinates of the image formed
in the rectangular coordinate plane after a point P undergoes the
transformations. [Nos. 22-24]
22. P(3 , -7) is translated 3 units downwards and then translated 1 unit
to the right.
23. P(4 , -2) is reflected in the x-axis and then translated 10 units
upwards.
24. P(-5 , 6) is translated 2 units to the left and then reflected in the
y-axis.
O
x
y
2
4
6
8
-2
-4
-6
2 4 6
-2-4-6
P(-3,- 4)
y
-4 -3 -2 -1 10
1
-1
2
3
2 3 4 x
A
B
C
y
-4 -3 -2 -1 10
1
-1
2
3
2 3 4 x
QP
R
S
y
-2 -1 1O
1
-1
-2
2
2 x
H
K
4
4
4
4
4
4
4
4
4
Al(-1 , 2), Bl(-2 , 3),
Cl(-3 , -1)
(-6 , 1)
(5 , -4)
(-5 , 3)
(4 , -10)
(4 , 12)
(7 , 6)
Pl(-1 , 3), Ql(-3 , 3),
Rl(-4 , 1), Sl(-2 , 1)
Hl(2 , 2), Kl(-1 , 1)
B'
C'
A'
P'
S'
R' Q'
K'
H'