Author:
LHasty
Rotation is a Rigid-Motion Transformation about a Point of Rotation at a given Angle of Rotation. Triangle ABC is rotated about Point O (0,0) Move Slider α for an Angle of Rotation between 0° and 360°.
1. What kind of a triangle is ABC ? _____________________________________. 2. What are the Coordinates for Points A, B, and C? Point A ( _____ , _____ ), Point B ( _____ , _____ ), and Point C ( _____ , _____ ). 3. Move the slider to 90°, what are the Coordinates for Points A’, B’, and C’? Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ). 4. Move the slider to 180°, what are the Coordinates for Points A’, B’, and C’? Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ). 5. Move the slider to 270°, what are the Coordinates for Points A’, B’, and C’? Point A’ ( _____ , _____ ), Point B’ ( _____ , _____ ), and Point C’ ( _____ , _____ ). 6. Compare and contrast coordinates for the above rotations: What remained the same _______________________________________________________ What changed? _______________________________________________________ 7. What do you notice about the slopes of the side AB and side BC ? ____________________________________________________________________________________ 8. Move Point A to change the orientation of the triangle ABC. Is the above relationship between coordinate points the same? What is Different ? ______________________________________________________________ ____________________________________________________________________________________ Next, be sure pre-image and rotated image is not onto itself (rotate 90°). Place cursor on A’ of rotated image, touch trackpad with two fingers for additional options, and select [Trace on], repeat for points B’ and C’. Place cursor on slider α, touch trackpad with two fingers for additional options, and select [Animation On] . What relationship exist between the pre-image points and the rotated image points with respect to the origin ? __________________________________________________________________________________________ To reset Trace, deselect [Animation On] and use two fingers on trackpad to scroll in or out. Move the Point of Rotation away from the origin. Does the same relationship exist between the pre-image points and the rotated image points with respect to the origin ? __________________________________________________________________________________________