Rectangular Coordinate System (I) 8.47
From Class Activity 8.6, if a point P(x , y) is rotated anticlockwise about
the origin O through 90c, 180c (i.e. 2 # 90c) and 270c (i.e. 3 # 90c),
then the coordinates of the images obtained are as follows:
Direction and
angle of rotation
Coordinates of
the image
anticlockwise, 90c (-y , x)
anticlockwise, 180c (-x , -y)
anticlockwise, 270c (y , -x)
y
x
O
P(x,y)
(-x,-y)
(y,-x)
(-y,x)
90°
90°
90°
90°
For rotation of a point P(x , y) clockwise about the origin O through
an angle i, the image Pl is the same as that obtained by rotating P
anticlockwise about O through an angle of (360c - i).
P
P'
rotate anticlockwise
by 360°- i
rotate clockwise by i
In particular, we have the following results:
P(x,y)
O
P'(y,- x)
clockwise
90°
anticlockwise
270°
P(x,y)
P'(- x,- y)
O clockwise
180°
anticlockwise
180°
P(x,y)
O
P'(- y,x) clockwise
270°
anticlockwise
90°
Think
What will the corresponding
images be when the angles
of rotation are 360c and
450c?
(a) P(4 , -7) is rotated about the origin O through 180c
to a point Q. Find the coordinates of Q.
(b) R(-2 , 5) is rotated anticlockwise about the origin O
through 90c to a point S. Find the coordinates of S.
(a) Diagram Clue
y
x
O
Q
P(4,-7)
180°
Coordinates of Q
= (,)47Level 1
Example 17 We could omit the direction
of rotation when the point is
rotated about O through 180c.
◀
From the sketch, the
signs of the coordinates
of Q: (- , +).
Solution
N28 The images are the same as
those obtained when the angles
of rotation are (360c - 360c)
and (450c - 360c), i.e. 0c and
90c. They are (x , y) and (-y , x)
respectively.
N28
[ Objective: Question related to rotation in a rectangular coordinate
plane.]
Supp Example 17
[on P.T8.76g]