1. Rotation
Objectives:
D Grade Rotate shapes about the origin
Describe rotations fully about the origin
Identify reflection symmetry in 3-D solids
C Grade Rotate shapes about any point
Describe rotations fully about any point
Find the centre of rotation and describe it fully

2. Rotation
In order to rotate an object we need 3 pieces of information
Centre of rotation
Angle of rotation
Direction of rotation
In order to find the image, using this information it is
best to use tracing paper.

3. Rotation Centre of rotation Angle of rotation 90o
Direction of rotation
clockwise
Put a piece of tracing paper
over the drawing
Copy the object onto the
tracing paper A A’
Put a pencil on the tracing
paper – point at the centre
of rotation X
Rotate the tracing paper
by the required amount in
the specified direction
Note the end point of the object.
Remove the tracing paper and
draw the image and label it.

4. If you are asked to rotate and object
Rotation
Centre of rotation
Angle of rotation
30o
Direction of rotation
clockwise
If you are asked to rotate and object
by an angle that you have to measure
follow the same steps and:
30o A’ A
Mark a line from the centre of rotation
to use as 0o and also mark this on the
same place on the tracing paper. X
Before putting the tracing paper on
measure the required angle, and draw
a line accordingly.

5. Now do these Rotation y-axis x-axis Rotate A :
90o c/w about the origin
and label it ‘a’
b) 180o c/w about the origin
and label it ‘b’
c) 90o anti c/w about the origin
and label it ‘c’
d) 90o c/w about the (2,2)
and label it ‘d’
e) 90o anti c/w about the (-2,1)
and label it ‘e’
f) 90o anti c/w about the (-4,6)
and label it ‘f’
g) 90o anti c/w about the (1,8)
and label it ‘g’
y-axis 1 2 3 4 5 6 7 8 9 10
x-axis -4 -5 -6 -7 -8 -9
-10 -3 -2 -1 x f d x A g a x x e x c b

6. Finding the centre of rotation Draw a line from each point
to the corresponding point
on the image. B C A
Object
Draw the perpendicular
bisector for the connecting
lines.
75o x
The centre of rotation is
where the perpendicular
bisectors cross. C’ B’ A’
75o anticlockwise
Image
The alternative (easier) method
is to trace the object onto tracing
paper and use trial and error

7. Now do these Rotation y-axis 90o c/w centre (0,0)
Find the centre of rotation for
each of these rotations
A onto B
A onto C
A onto D
D onto B
B onto F
A onto E
C onto G
H onto A
B onto E
D onto C
y-axis 1 2 3 4 5 6 7 8 9 10
x-axis -4 -5 -6 -7 -8 -9
-10 -3 -2 -1 A B F G H C D
90o c/w centre (0,0) E
180o c/w or ac/w centre (0,0)
270o c/w or 90o ac/w centre (0,0)
270o c/w or 90o ac/w centre (0,0)
90o c/w centre (2,-2)
90o ac/w centre (2,6)
90o c/w centre (-2,-1)
180o c/w or ac/w centre (0,4)
180o c/w or ac/w centre (4,2)
90o ac/w centre (0,0)

8. Worksheet 1 Rotation A Rotate shape A : 90o c/w about the origin
and label it ‘a’
b) 180o c/w about the origin
and label it ‘b’
c) 90o anti c/w about the origin
and label it ‘c’
d) 90o c/w about the (2,2)
and label it ‘d’
e) 90o anti c/w about the (-2,1)
and label it ‘e’
f) 90o anti c/w about the (-4,6)
and label it ‘f’
g) 90o anti c/w about the (1,8)
and label it ‘g’
Find the centre of rotation for
each of these rotations
A onto B
b) A onto C
c) A onto D
d) D onto B
e) B onto F
f) A onto E
C onto G
H onto A
B onto E
D onto C A 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3
-10 1 2 -2 -1 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3
-10 1 2 -2 -1 A B F G H C D