http://www.ck12.org Chapter 12. Rigid Transformations
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter12RotationsB
Concept Problem Revisited
The center of rotation is shown in the picture below. If we draw rays to the same point in each arrow, we see that the
two images are a 120◦rotation in either direction.
Vocabulary
Atransformationis an operation that moves, flips, or otherwise changes a figure to create a new figure. Arigid
transformation(also known as anisometryorcongruence transformation) is a transformation that does not
change the size or shape of a figure. The new figure created by a transformation is called theimage. The original
figure is called thepreimage. Arotationis a transformation where a figure is turned around a fixed point to create
an image. The lines drawn from the preimage to thecenter of rotationand from the center of rotation to the image
form theangle of rotation.
Guided Practice
- The rotation of a quadrilateral is shown below. What is the measure ofxandy?
- A rotation of 80◦clockwise is the same as what counterclockwise rotation?
- A rotation of 160◦counterclockwise is the same as what clockwise rotation?
Answers:
- Because a rotation is an isometry that produces congruent figures, we can set up two equations to solve forxand
y.
2 y= 80 ◦ 2 x− 3 = 15
y= 40 ◦ 2 x= 18
x= 9- There are 360◦around a point. So, an 80◦rotation clockwise is the same as a 360◦− 80 ◦= 280 ◦rotation
counterclockwise. - 360◦− 160 ◦= 200 ◦clockwise rotation.
Practice
In the questions below, every rotation is counterclockwise,
- If you rotated the letterp 180 ◦counterclockwise, what letter would you have?