Copy of Rotations
A rotation is a transformation that creates a new figure through "turning" a figure around a given point.
The point is called the "center of rotation." Rays drawn from the center of rotation to a point and its image form the "angle of rotation."
Summary: Change the angle of rotation by moving the green slider (make sure to check the rotation box). Notice:
Do the angles change? If so, how?
Do the segments change? If so, how?
Do the points change? If so, how?
Now, return to the GeoGebra sketch above. Use the slider to focus on 90˚, 180˚, and 270˚counter-clockwise rotations. Notice how the points change and record your findings below.
For a 90˚ counterclockwise rotation, the rule for changing each point is
For a 180˚ counterclockwise rotation, the rule for changing each point is
For a 270˚ counterclockwise rotation, the rule for changing each point is
Clockwise Rotations
Clockwise Rotations
For a 90 clockwise rotation, the rule for changing each point is
For a 180 clockwise rotation, the rule for changing each point is
For a 270 clockwise rotation, the rule for changing each point is
Can you do it on your own?
Use the GeoGebra tools to create a polygon and a point at the origin.
1.Use this button to create a polygon. 
2. Use this button to plot a point at (0,0).
Then rotate your shape 180˚ counterclockwise.
3. Use these buttons to Rotate your polygon. 
then 
4. Select the image first, then the origin point. It will then prompt you for the angle of rotation.
2. Use this button to plot a point at (0,0).
Then rotate your shape 180˚ counterclockwise.
3. Use these buttons to Rotate your polygon. then
4. Select the image first, then the origin point. It will then prompt you for the angle of rotation.
Check your understanding
What counter-clockwise angle of rotation was used to move ABCD to A'B'C'D'?
Challenge!
The challenge today is to explore a variety of compositions of transformations.
Rotations and Reflections
Create a triangle with vertices A(1,1) B (2,3) C (4,1).
1. Use 
and select polygon to create a triangle with vertices A(1,1) B (2,3) C (4,1).
Reflect the triangle over the y-axis.
2.Use 
and select "Reflect about line", Click the Triangle, then click the y-axis.
Rotate the reflected image 90 counter clockwise.
(Refer to previous tasks for directions)
and select polygon to create a triangle with vertices A(1,1) B (2,3) C (4,1).
Reflect the triangle over the y-axis.
2.Use and select "Reflect about line", Click the Triangle, then click the y-axis.
Rotate the reflected image 90 counter clockwise.
(Refer to previous tasks for directions)
What are the new vertices of the reflected then rotated triangle?