Transformation: Rotation

Unit 4.10

I can perform rotations and identify their transformation notation.

Vocabulary Rotation: A transformation where a

figure is turned around a fixed point to create a new image. The lines drawn from the original figure

to the center of rotation, and from the center of rotation to the final figure form the angle of rotation.

Example:

Something to Remember:

In this Unit, we will only rotate counter clock-wise

unless otherwise specified!

Do you know? 80° clock-wise rotation = _______°

counter clock-wise rotation?

How do you know?

Answer: The Key: 360°

Try this one! 200° clock-wise rotation = _______°

counter clock-wise rotation?

How do you know?

Answer: The Key: 360°

Vocabulary Rotation on the Coordinate Plane:

To rotate a figure in the coordinate plane, we use the origin as the center of rotation.

Example: Rotate segment AB 180° when A(7, 4) and B(6, 1). Find the coordinates of A’ and B’.

Example: Rotate segment AB 180° when A(7, 4), and B(6, 1). Find the coordinates of A’ and B’.

A’ = __________

B’ = ___________

B

A

What do you notice about the

coordinates? (180°)A(7, 4) A’(–7, –4)

and

B(6, 1) B’(–6, –1)

In other words:(x, y) (–x, –y)

Example

Let’s Try Another! Rotate ΔABC 90° when A(6, –1), B(2, –8), and C(1, –1). Find the coordinates of A’, B’ and C’.

A’ = __________

B’ = __________

C’ = __________

C

B

A

What do you notice about the

coordinates? (90°)A(6, –1) A’(1, 6)B(2, –8) B’(8,2)C(1, –1) C’(1, 1)

In other words:(x, y) (–y, x)

Example

Let’s Try Another! Rotate ΔABCD 270° when A(–4, 5), B(1, 2), C(–6, –2) and D(–8, 3). Find all prime coordinates. Hint: 270° =

90°+180°

A’ = __________

B’ = __________

C’ = __________

D’ = __________

B

A

C

D

What do you notice about the

coordinates? (270°)A(–4, 5) A’(5, 4)B(1, 2) B’(2, –1)

C(–6, –2) C’(–2, 6)D(–8, 3) D’(3, 8)

In other words:(x, y) (y, –x)

Example

A

B

C

A’B’

C’

Rotate ΔABC counter clock-wise 90°. Label the new image, ΔA’B’C’ and list the coordinates below.

A: _____________

B: _____________

C: ____________

A’: ____________

B’: ____________

C’: ____________

(9,-2)

(8,-7)

(1,-1)

(2,9)

(7,8)

(1,1)

1)90° Rule: (x,y) (-y,x)

H

I

G

H’I’

G’

Rotate ΔGHI 270° counter clock-wise. Label the new image, ΔG’H’I’ and list the coordinates below.

G: ____________

H: _____________

I: ______________

G’: ____________

H’: ____________

I’: _____________

(1,5)

(7,7)

(6,2)

(5,-1)

(7,-7)

(2,-6)

270° Rule: (x,y) (y,-x)

2)

M

NP

Rotate polygon MNOP 180° counter clock-wise. Label the new image, M’N’O’P’ and list the coordinates below.

M: ____________

N: _____________

O: ____________

P: _____________

M’: ____________

N’: ____________

O’: ____________

P’: ____________

(4,9)(8,5)

(1,1)

(-4,-9)

(-8,-5)(-1,-1)

3)

180° Rule: (x,y) (-x,-y)

O

M’

N’P’

O’

(1,5)

(-1,-5)

Homework Time Turn It! -- Rotation WS

I can perform rotations and identify their transformation notation.