Graphing Transformations 3

Rotation – the motion of an object around a fixed point

Direction of rotation – can be clockwise or counter-clockwise

Centre of rotation – the fixed point around which the rotation takes place

Angle of rotation – the amount of rotation made

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

360°

centre of rotation

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

90°

270°

counter-clockwise

clockwise-270°

+90°

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

180° counter-clockwise

180° clockwise-180°

+180°

TOP OF PAGE

A rotation +90°

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

A rotation +180°

TOP OF PAGE

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

A rotation +270°

TOP OF PAGE

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

Would the images be different if the figures had been rotated clockwise instead of counter-clockwise?

A rotation -90°

TOP OF PAGE

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

Would the images be different if the figures had been rotated clockwise instead of counter-clockwise?

A 90° clockwise rotation produces the same image as a 270° counter-clockwise rotation, and vice versa.

Coordinates

A

B

C

DA’

B’

C’

D’A(0,1)B(2,3)C(4,2)D(3,0)1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A’(-1,0)B’(-3,2)C’(-2,4)D’(0,3)

A rotation +90° OR -270°

What patterns do you see in the coordinates of the figure and its image?

• x-coordinates and y-coordinates switched and the x-coordinates have the opposite sign

Coordinates

A

B

C

D

A’

B’

C’

D’

A(0,1)B(2,3)C(4,2)D(3,0)1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A’(0,-1)B’(-2,-3)C’(-4,-2)D’(-3,0)

A rotation +180° OR -180°

What patterns do you see in the coordinates of the figure and its image?

• x-coordinates and y-coordinates have the opposite sign

Coordinates

A

B

C

D

A’

B’

C’

D’

A(0,1)B(2,3)C(4,2)D(3,0)1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A’(1,0)B’(3,-2)C’(2,-4)D’(0,-3)

A rotation +270° OR -90°

What patterns do you see in the coordinates of the figure and its image?

• x-coordinates and y-coordinates switched and the y-coordinates have the opposite sign

How are a figure and its rotation image alike?• They are congruent. • They have the same orientation. If ABCD is read clockwise, then A’B’C’D’ is read clockwise.

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A

B

C

D

Rotate ABCD -90°

Coordinates

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

xA

B

C

D

Rotate ABCD +270°

Coordinates

1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A

B

C

D

Rotate ABCD 180°

Coordinates

Coordinates

A

B

C

D

A(0,1)B(2,3)C(4,2)D(3,0)1

4-4 1 2 3

4

3

2

-3 -1-2

-1

-2

-4

-3

y

x

A rotation