2.6.2 Rotations and Compositions
- 1. Rotations & Compositions The student is able to (I can): • Identify and draw rotations • Identify and draw compositions of transformations
- 2. rotationrotationrotationrotation – a transformation that turns a figure around a fixed point, called the center of rotation. • center of rotation
- 3. In the coordinate plane, we will look at two specific types of rotations: 90° about the origin 180° about the origin x y • P(x, y) P´(–y, x) • 90909090°°°° • P´(–x, –y) 180180180180°°°° ( , ) ( , )x y y x→ − ( , ) ( , )x y x y→ − −
- 4. Examples 1. Rotate ΔRUG with vertices R(2, -1), U(4, 1), and G(3, 3) by 90° about the origin. 90°: 2. Rotate ΔTRI with vertices T(2, 2), R(4, -5), and I(-1, 6) by 180° about the origin. 180°: ( , ) ( , )x y y x→ − ( , ) ( , )x y x y→ − −
- 5. Examples 1. Rotate ΔRUG with vertices R(2, -1), U(4, 1), and G(3, 3) by 90° about the origin. 90°: RRRR´´´´(1, 2),(1, 2),(1, 2),(1, 2), UUUU´´´´((((----1, 4),1, 4),1, 4),1, 4), GGGG´´´´((((----3, 3)3, 3)3, 3)3, 3) 2. Rotate ΔTRI with vertices T(2, 2), R(4, -5), and I(-1, 6) by 180° about the origin. 180°: TTTT´´´´((((----2,2,2,2, ----2),2),2),2), RRRR´´´´((((----4, 5),4, 5),4, 5),4, 5), IIII´´´´(1,(1,(1,(1, ----6)6)6)6) ( , ) ( , )x y y x→ − ( , ) ( , )x y x y→ − −
- 6. When performing a rotation that is notnotnotnot based on multiples of 90°, you will need to use a protractor to measure the angles, and then draw the image. Example: Rotate the figure 60° about P. •P
- 7. Example: Rotate the figure 60° about P. Step 1: Draw a line from P to a vertex. •P
- 8. Example: Rotate the figure 60° about P. Step 1: Draw a line from P to a vertex. Step 2: Use protractor to measure a 60° angle. You can use a ruler or a compass to set the length. •P
- 9. Example: Rotate the figure 60° about P. Step 1: Draw a line from P to a vertex. Step 2: Use protractor to measure a 60° angle. You can use a ruler or a compass to set the length. Step 3: Repeat for the other vertices. •P
- 10. composition ofcomposition ofcomposition ofcomposition of transformationstransformationstransformationstransformations – performing two or more transformations sequentially (one after another) to a figure. An example of a composition is a glideglideglideglide reflectionreflectionreflectionreflection: we reflect the figure and then translate it along a vector.