Which one of the following figures represents a rotation? Explain.
Watch This
First watch this video to learn about rotations.
CK12 Foundation Chapter10RotationsA
Then watch this video to see some examples.
CK12 Foundation Chapter10RotationsB
Guidance
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) 



Example A
Describe the rotation of the blue triangle in the diagram below.
Solution: Looking at the angle measures,
Example B
Describe the rotation of the triangles in the diagram below.
Solution: Looking at the angle measures,
Example C
Describe the rotation in the diagram below.
Solution: To describe the rotation in this diagram, look at the points indicated on the S shape.
 Points
BC :B(−3,4) C(−5,0)  Points
B′C′ :B′(4,3) C′(0,5)
These points represent a rotation of
Concept Problem Revisited
Which one of the following figures represents a rotation? Explain.
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
Vocabulary
 Center of rotation
 A center of rotation is the fixed point that a figure rotates about when undergoing a rotation.
 Rotation
 A rotation is a transformation that rotates (turns) an image a certain amount about a certain point.
 Image
 In a transformation, the final figure is called the image.
 Preimage
 In a transformation, the original figure is called the preimage.
 Transformation
 A transformation is an operation that is performed on a shape that moves or changes it in some way. There are four types of transformations: translations, reflections, dilations and rotations.
Guided Practice
1. Describe the rotation of the pink triangle in the diagram below.
2. Describe the rotation of the blue polygon in the diagram below.
3. Describe the rotation of the green hexagon in the diagram below.
Answers:
1. Examine the points of the preimage and the rotated image (the blue triangle).
Points on 



Points on 



These points represent a rotation of
2. 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
3. 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 \begin{align*}D \ 90^\circ\end{align*} clockwise. You would say that the green hexagon is rotated \begin{align*}90^\circ\end{align*}CW to form the orange hexagon.
Practice
If the following points were rotated about the origin with a \begin{align*}180^\circ\end{align*}CCW rotation, what would be the coordinates of the rotated points?
 (3, 1)
 (4, 2)
 (5, 3)
 (6, 4)
 (3, 3)
If the following points were rotated about the origin with a \begin{align*}90^\circ\end{align*}CW rotation, what would be the coordinates of the rotated points?
 (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 \begin{align*}180^\circ\end{align*}?