Which one of the following figures represents a rotation? Explain.

### Rotations

In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees. The figure below shows that the Preimage A has been rotated

In order to describe a rotation, you need to state how many degrees the preimage rotated, the center of rotation, and the direction of the rotation (clockwise or counterclockwise). The most common center of rotation is the origin. The table below shows what happens to points when they have undergone a rotation about the origin. The angles are given as counterclockwise.

Center of Rotation |
Angle of Rotation |
Preimage (Point |
Rotated Image (Point |
---|---|---|---|

(0, 0) | |||

(0, 0) | |||

(0, 0) |

#### Let's describe the following rotations:

- The rotation of the blue triangle in the diagram below.

Looking at the angle measures,

- Image A to image B

Looking at the angle measures,

- The rotation in the diagram below.

To describe the rotation in this diagram, look at the points indicated on the S shape.

Points

Points

These points represent a rotation of

### Examples

#### Example 1

Earlier, you were shown following three figures and asked which one of the figures represents a rotation.

You know that a rotation is a transformation that turns a figure about a fixed point. This fixed point is the turn center or the center of rotation. In the figures above, Figure 1 and Figure 3 involve turning the heart about a fixed point. Figure 1 rotates the heart about the point

#### Example 2

Describe the rotation of the pink triangle in the diagram below.

Examine the points of the preimage and the rotated image (the blue triangle).

Points on |
|||

Points on |

These points represent a rotation of

#### Example 3

Describe the rotation of the blue polygon in the diagram below.

For this image, look at the rotation. It is not rotated about the origin but rather about the point

The blue polygon is being rotated about the point

#### Example 4

Describe the rotation of the green hexagon in the diagram below.

For this image, look at the rotation. It is not rotated about the origin but rather about the point

The green polygon is being rotated about the point

### Review

If the following points were rotated about the origin with a

- (3, 1)
- (4, -2)
- (-5, 3)
- (-6, 4)
- (-3, -3)

If the following points were rotated about the origin with a

- (-4, 3)
- (5, -4)
- (-5, -4)
- (3, 3)
- (-8, -9)

Describe the following rotations:

- Why is it not necessary to specify the direction when rotating
180∘ ?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 10.7.