http://www.ck12.org Chapter 12. Rigid Transformations
12.4 Rotations
Here you’ll learn what a rotation is and how to find the coordinates of a rotated figure.
What if you wanted to find the center of rotation and angle of rotation for the arrows in the international recycling
symbol below? It is three arrows rotated around a point. Let’s assume that the arrow on the top is the preimage and
the other two are its images. Find the center of rotation and the angle of rotation for each image. After completing
this Concept, you’ll be able to answer these questions.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter12RotationsA
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Click image to the left for more content.Brightstorm:Rotations
Guidance
Atransformationis an operation that moves, flips, or changes a figure to create a new figure. Arigid transforma-
tionis a transformation that preserves size and shape. The rigid transformations are: translations, reflections, and
rotations (discussed here). The new figure created by a transformation is called theimage. The original figure is
called thepreimage. Another word for a rigid transformation is anisometry. Rigid transformations are also called
congruence transformations. If the preimage is A, then the image would be labeled A′, said “a prime.” If there is
an image of A′, that would be labeled A′′, said “a double prime.”
Arotationis a transformation by which a figure is turned around a fixed point to create an image. Thecenter of
rotationis the fixed point that a figure is rotated around. Lines can be drawn from the preimage to the center of
rotation, and from the center of rotation to the image. The angle formed by these lines is theangle of rotation.
In this Concept, our center of rotation will always be theorigin.Rotations can also be clockwise or counterclock-
wise. We will only docounterclockwiserotations, to go along with the way the quadrants are numbered.
Investigation: Drawing a Rotation of
Tools Needed: pencil, paper, protractor, ruler