Identify and draw rotations

1. Rotations
The student is able to (I can):
• Identify and draw rotations

2. rotation 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:
90º about the origin
180º about the origin
x
y
•
P(x, y)
P´(—y, x)
•
90º90º90º90º
•
P´(—x, —y)
180º180º180º180º
(x, y) ( y,x)→ −
(x, y) ( x, y)→ − −

4. Examples 1. Rotate ∆RUG with vertices R(2, -1),
U(4, 1), and G(3, 3) by 90º about the
origin.
90º:
RRRR´´´´(1, 2), U(1, 2), U(1, 2), U(1, 2), U´´´´((((----1, 4), G1, 4), G1, 4), G1, 4), G´´´´((((----3, 3)3, 3)3, 3)3, 3)
2. Rotate ∆TRI with vertices T(2, 2),
R(4, -5), and I(-1, 6) by 180º about the
origin.
180º:
TTTT´´´´((((----2,2,2,2, ----2), R2), R2), R2), R´´´´((((----4, 5), I4, 5), I4, 5), I4, 5), I´´´´(1,(1,(1,(1, ----6)6)6)6)
(x, y) ( y,x)→ −
(x, y) ( x, y)→ − −

5. 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

6. Example: Rotate the figure 60° about P.
Step 1: Draw a line from P to a vertex.
•P

7. 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

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.
Step 3: Repeat for the other vertices.
•P