Rectangular Coordinate System (I) 8.51
3. In the figure, the origin O is the centre of rotation. Complete the table
below. Original
point
Direction of
rotation
Angle of
rotation
Coordinates of
the image
(a) A clockwise 90c ( , )
(b) B clockwise 180c ( , )
(c) C anticlockwise 270c ( , )
4. (a) P(2 , -3) is translated 3 units to the left and then 2 units
upwards to a point Q. Find the coordinates of Q.
(b) R(-7 , 6) is reflected in the x-axis and then reflected in the
y-axis to a point S. Find the coordinates of S.
5. (-7 , 2) is the image of a point K when K is rotated about the origin O
through 180c. Find the coordinates of K.
Exercise 8D
Level 1
1. Refer to the figure. Find the coordinates of the image after the
following translations.
(a) The point P is translated 6 units to the right.
(b) The point P is translated 2 units to the left.
2. Refer to the figure. Find the coordinates of the image after the
following translations.
(a) The point Q is translated 1 unit upwards.
(b) The point Q is translated 4 units downwards.
3. X(-4 , 7) is translated 8 units to the right to a point Y. Y is then
translated 2 units upwards to a point Z. Find the coordinates of Y
and Z.
4. A(-2 , 6) is translated 7 units downwards and then 4 units to the left
to a point B. Find the coordinates of B.
y
x
O
-5
5
5
-5
A B
C
D
90°
90°
90°
90°
y
x
O
P(-4,2)
➥ Example 12
y
x
O
Q(2,1)
Level 0
Level 0
1
1
1
1
Exercise Objective
1 Questions related to translation in a rectangular coordinate plane.
2 Questions related to reflection in a rectangular coordinate plane.
3 Questions related to rotation in a rectangular coordinate plane.
4 Miscellaneous questions.
Consolidation Ex 8D
Exam-type
question
Reference
TSA
Q1, Q2
2019 (ME1) Q36,
2018 (ME1) Q36
Q6, Q7
2019 (ME2) Q16,
2017 (ME3) Q17
Q8-Q12
2018 (ME2) Q16,
2016 (ME2) Q17
DSE
Q25(a),
Q27(a)
2017 (I) Q6(a),
2014 (I) Q8(a)
(2 , 2)
(2 , 2)
(-6 , 2)
(2 , -3)
Y(4 , 7), Z(4 , 9)
(-6 , -1)
(-1 , -1)
(7 , -6)
(7 , -2)
4
4
-4
5
5
-5