Rectangular Coordinate System (I) 8.57
Note Example
(b) Reflection of a point P(x , y)
Axis of reflection
Coordinates of the
image
x-axis (x , -y)
y-axis (-x , y)
Reflect in a horizontal line l:
P'(x,y + 2a)
P(x,y)
m
a units
a units
P'(x,y - 2a)
P(x,y)
m
a units
a units
Reflect in a vertical line L:
Q(x,y) Q'(x + 2b,y)
L
b units b units
Q(x,y)
Q'(x - 2b,y) L
b units b units
(c) Rotation of a point P(x , y) about the origin
Direction and angle
of rotation
Coordinates of
the image
anticlockwise, 90c
(or clockwise, 270c)
(-y , x)
anticlockwise, 180c
(or clockwise, 180c)
(-x , -y)
anticlockwise, 270c
(or clockwise, 90c)
(y , -x)
y
x
O
K(2,1)
H(- 2,1)
H(-2 , 1) is reflected in the y-axis to a point K.
Then
coordinates of K = (-(-2) , 1)
= (2 , 1)
y
x
O
F(2 ,5)
E(2,-1)
(- 2,2)
m
3 units
3 units
l is a line parallel to the x-axis and passes
through (-2 , 2). E(2 , -1) is reflected in l to a
point F. Then
distance between E and l = [2 - (-1)] units
= 3 units
coordinates of F = (2 , -1 + 2 # 3)
= (2 , 5)
y
x
O
T(4,-1)
S(-1,-4)
90°
S(-1 , -4) is rotated anticlockwise about the
origin O through 90c to a point T. Then
coordinates of T = (-(-4) , -1)
= (4 , -1)