Quadrilateral
Watch This
First watch this video to learn about graphs of rotations.
CK12 Foundation Chapter10GraphsofRotationsA
Then watch this video to see some examples.
CK12 Foundation Chapter10GraphsofRotationsB
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.
For now, in order to graph a rotation in general you will use geometry software. This will allow you to rotate any figure any number of degrees about any point. There are a few common rotations that are good to know how to do without geometry software, shown in the table below.
Center of Rotation  Angle of Rotation 
Preimage (Point 
Rotated Image (Point 

(0, 0) 



(0, 0) 



(0, 0) 



Example A
Line
Solution:
Example B
The diamond
Solution:
Notice the direction is counterclockwise.
Example C
The following figure is rotated about the origin
Solution:
Notice the direction of the rotation is counterclockwise, therefore the angle of rotation is
Concept Problem Revisited
Quadrilateral
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. Line
2. The polygon below has been rotated
3. The purple pentagon is rotated about the point
Answers:
1.
Notice the direction of the angle is clockwise, therefore the angle measure is
2.
Notice the direction of the angle is counterclockwise, therefore the angle measure is
3.
The measure of
Practice
 Rotate the above figure
90∘ clockwise about the origin.  Rotate the above figure
270∘ clockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ counterclockwise about the origin.  Rotate the above figure
270∘ counterclockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ clockwise about the origin.  Rotate the above figure
270∘ clockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ counterclockwise about the origin.  Rotate the above figure
270∘ counterclockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ clockwise about the origin.  Rotate the above figure
270∘ clockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ counterclockwise about the origin.  Rotate the above figure
270∘ counterclockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ clockwise about the origin.  Rotate the above figure
270∘ clockwise about the origin.  Rotate the above figure
180∘ about the origin.
 Rotate the above figure
90∘ counterclockwise about the origin.  Rotate the above figure
270∘ counterclockwise about the origin.  Rotate the above figure
180∘ about the origin.