Identify and draw rotations Identify and draw compositions of transformations

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.