Isometric Transformations: Rotations
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- Brenda Mills
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1 1. What kind of angle is this? Isometric Transformations: Rotations Rotation: transformation that turns the plane through a given angle about (around) a given point. In other words, a translation is a turn around a center point. The angle is called the angle of rotation and the point around which the plane is turned is called the center point of rotation. ut before we start spinning around, lets talk about angles and clocks. 2. How many degrees does it measure? What kind of angle is this? How many degrees does it measure? 3. How many degrees are there in a quarter rotation clockwise? 4. How many degrees are there in a quarter rotation counter-clockwise? We can also say this is a -90 rotation. We can also say this is a 90 rotation. 5. How many degrees are there in a half rotation counter-clockwise? 6. How many degrees are there in a half rotation clockwise? We can also say this is a 180 rotation. We can also say this is a -180 rotation LetsPracticeGeometry.com
2 irections: Use patty paper, Geometry software, or any other method available to you to rotate each figure as directed. Make sure to label your new figure. 1. Rotate 90 clockwise about the origin. 2. Rotate 90 counter-clockwise about the origin. R O,90 3. Rotate 180 clockwise about the origin. R O, Rotate 180 counter-clockwise about the origin. R O,180 5a. What do you think happens to the center point of rotation? oes it move? 6. Is a rotation an isometric transformation? b. What do think is each points in image the same distance from the center as in the Why? LetsPracticeGeometry.com
3 irections: Use patty paper, Geometry software, or any other method to rotate each figure as directed. Make sure to label your image figure correctly. 1. Rotate UG 180 clockwise about the origin. R O, Rotate HF 180 counter-clockwise about the origin. R O,180 G U H F 3. Rotate H 90 clockwise about the origin. 4. Rotate 90 counter clockwise about the origin. R O,90 H 5. Rotate TO 90 clockwise about the origin. 6 Rotate Y 90 counter- clockwise about the origin. R O,90 Y T O LetsPracticeGeometry.com
4 irections: Refer to some of the problems on the previous page to help you make conjectures about the functions of rotations about the origin. 7. For problem 1 (180 rotation clockwise) 8. For problem 5 (90 rotation clockwise) (, ) U (, ) G (, ) (, ) U (, ) G (, ) escribe the relationship between the original T (, ) O (, ) (, ) T (, ) O (, ) (, ) escribe the relationship between the original escribe the relationship with a function. 9. For problem 5 (90 rotation counter clockwise) escribe the relationship with a function. 10. ill says if you rotate a figure 180 clockwise or counterclockwise you will get the same image. Sally says you won t. Who is correct? Why? (, ) (, ) Y (, ) (, ) (, ) Y (, ) escribe the relationship between the original escribe the relationship with a function LetsPracticeGeometry.com
5 irections: We can also rotate figures around other points. Use patty paper, Geometry software, or any other method to rotate each figure as directed. Make sure to label figure. 1. Rotate OW 180 clockwise about point P. R p, Rotate R 90 counter-clockwise about point S. R S,90 W O P S R 3. Rotate IK 90 counter-clockwise about 4. Rotate 90 clockwise about point. the point K. R K,90 R,-90 I K 5. Rotate 180 counter-clockwise about 6. Rotate PIN 90 clockwise about point R. point Y. R Y,180 R R,-90 W X P Z Y R N I LetsPracticeGeometry.com
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