Rotation is a Rigid-Motion Transformation [br]about a Point of Rotation at a given Angle of Rotation.[br][br]Triangle ABC is rotated about Point O (0,0)[br]Move Slider α for an Angle of Rotation between 0° and 360°.

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