Rectangular Coordinate System (I) 8.55
26. The figure shows a horizontal line segment MN with end points
M(-3 , -1) and N(1 , -1). M and N are reflected in the line l to Ml
and Nl respectively.
(a) Find the coordinates of Ml and Nl.
(b) Draw MMl and MlNl in the figure. Is MMl perpendicular to
MlNl? Explain your answer.
27. P(1 , 7), Q(1 , -2) and R(-4 , -2) are rotated anticlockwise about
the origin O through 90c to Pl, Ql and Rl respectively.
(a) Find the coordinates of Pl, Ql and Rl.
(b) Ivan claims that +PQR = +PlQlRl. Do you agree? Explain
your answer.
28. E(8 , -1) undergoes a transformation to reach F(-8 , -1). Describe
two possible transformations.
29. R(-2 , 2) is the image after P(6 , -2) undergoes two transformations.
Describe the possible transformations.
Level 3
30. D(5 , -3) is translated vertically by a units to a point E, and E is
then translated horizontally by b units to a point F. Afterwards, F is
rotated clockwise about the origin O through 90c to a point G. If D
and G coincide, find the values of a and b.
31. X(2 , 4) is reflected in the y-axis to a point Y, and Y is then reflected
in the x-axis to a point Z. Afterwards, Z is rotated clockwise about
the origin O through 630c to a point W.
(a) Find the coordinates of W.
(b) If X can also undergo each of the following transformations
below to reach W, describe the transformation(s).
(i) 2 translations
(ii) A rotation about O
(iii) A reflection in a horizontal line and then a translation
y
x
-1
1
2
-1-2-3-4
3
1
N
M
m
0
Explain
Explain
➥ Example 19
Openended
2
3
4
4
4
4
Level 3 Guiding Worksheet - Ex 8D Ml(-3 , 3), Nl(1 , 3)
Pl(-7 , 1), Ql(2 , 1), Rl(2 , -4)
yes
yes
E is reflected in the y-axis to F.
E is translated 16 units to the left to F.
P is first reflected in the x-axis, and
then translated to the left by 8 units
to R. (or other reasonable answers)
a = 8, b = 2
(4 , -2)
X is first translated 2 units to the right and then 6 units
downwards to W. (or other reasonable answers)
X is rotated clockwise about O through 90c to W. (or other reasonable answers)
X is first reflected in the horizontal line passing through (2 , 1), and then
translated to the right by 2 units to W. (or other reasonable answers)
[Clue: Question 30
Since D(5 , -3) and G coincide, the
coordinates of G are (5 , -3). By considering
the reverse process of the transformations
and with the help of a sketch, find the
coordinates of F and then the coordinates of
E. Thus, the values of a and b will be found.]
[Clue: Question 31
(a) The positions of X, Y,
Z and W are shown
in the figure. Find
the coordinates of Y
and Z. Hence, find
the coordinates of W.
(b) (i) Refer to the figure.
X may undergo
translations �①
and ② to reach W.
O
W
Z
Y X(2,4)
270°
x
y
O
W
X
x
y ① ②
(ii) Refer to the figure.
X undergoes a
rotation to reach W.
(iii) In the figure,
XN = NA and
line l #
x-axis # AW.
X undergoes a
reflection in
l and then a
translation to
reach W. ]
O
W
X
x
y
O
WA N
X
x
y
m
M' N'