1. Transformation Unit, Lesson ?
Rotations
Transformation Unit, Lesson ?

2. Rotations
A rotation is a transformation that turns a figure about a fixed point called the center of rotation.
An object and its rotation are the same shape and size, but the figures may be turned in different directions. (Rotations are isometric!!!)

3. Rotations
Amusement rides, such as the swing and the Ferris wheel, allow you to experience the concept of rotation.

4. Rotations
Rotations can be seen in nature.  The leaf on this plant illustrates the concept of a rotation.
The center of rotation is the point where the leaf is attached to the stem.

5. Rotations
Rotations can be seen in planetary movement.

6. Rotations
In mathematics, the rotation of an object is called its image.  If the original object was labeled with letters, such as polygon ABCDE, the image may be labeled with the same letters followed by a prime symbol, A'B'C'D'E'. 

7. Rotations Rotations can occur in either a clockwise
or counterclockwise direction.
When working in the coordinate plane, assume the center of rotation to be the origin unless told otherwise.
This rotation is  90°counterclockwise.

8. Remember: Rotations are TURNS!!!
A positive angle of rotation turns the figure counterclockwise, and a negative angle of rotation turns the figure in a clockwise direction.  The figure does not change size.
Remember: Rotations are TURNS!!!

9. Rotations
Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation. (notation Rdegrees )

10. Rotations Properties preserved under a rotation:
distance (lengths of segments are the same)
angle measures (remain the same)
parallelism (parallel lines remain
parallel)
colinearity (points stay on the same lines)
midpoint (midpoints remain the same in each figure)
orientation (lettering order remains the same)

11. Rotations
To work with rotations, you need to be able to recognize angles of certain sizes and understand the basic workings of a unit circle.
You should be able to recognize and reproduce the approximate size of a right angle (90 degrees), a 45 degree angle, a 30 degree angle and a 60 degree angle.

12. Rotations The radius of a unit circle is one (one unit).
Notice that degree movement on a unit circle goes in a counter-clockwise direction. 
You will want to remember the layout of the unit circle when you are graphing figures and their rotations.

13. Rotations Rotation of 90°: R90°(x, y) = (-y, x) Rotation of 180°:
R180°(x, y) = (-x, -y) [same as point reflection across origin]
Rotation of 270°:
R270°(x, y) = (y, -x)