1. 7.6 Rotations & Rotational
Symmetry

2. What is a Rotation?
A rotation is a turn around a point called the centre of rotation. We can rotate an object/shape either clockwise or counterclockwise.
When a figure is rotated:
The lengths of its sides are unchanged.
The measures of its angles are unchanged.
The orientation is unchanged.
The rotation image is congruent to the original figure.
Each point and its rotation image are the same distance from the centre of rotation.

3. Notice that the unit circle moves in a counter-clockwise direction.
To work with rotations, you need to be able to recognize angles of certain sizes and understand the basic workings of a unit circle.
Notice that the unit circle moves in a counter-clockwise direction.

4. Something to think about…
One complete rotation is 360°.
Which clockwise rotation is the same as a 90° counterclockwise rotation?
Which clockwise rotation is the same as a 270° counterclockwise rotation?
Which clockwise rotation is the same as a 180° counterclockwise rotation?

5. Quadrant
What are the signs (+ or-) within each quadrant of each x and y value?
(-,+)
(+,+)
(-,-)
(+,-)

6. The Process Step 1: Switch the numbers. Step 2: Determine the signs.
(-2,+3)
(+3,+2)
(-3,-2)
(+2,-3)

7. Example
Find the coordinates of the image of each point after a counterclockwise rotation of 90° about the origin.
A(3, 7)
B(0, 3)
C(6, -5) A C' B A' B' C

8. Example
Find the coordinates of the image of each point after a counterclockwise rotation of 180° about the origin.
A(3, 7)
B(0, 3)
C(6, -5) A C' B B' C A'

9. Example
Find the coordinates of the image of each point after a counterclockwise rotation of 270° about the origin.
A(3, 7)
B(0, 3)
C(6, -5) A B B' A' C' C

10. Example
Find the coordinates of the image of each point after a counterclockwise rotation of 90° about the point P(3,-2).
A(3, 7)
B(0, 3)
C(6, -5) A B 3 C' 5 A' 5 P 3 B' C

11. Example
Draw the quadrilateral with vertices C(3, 4), D(-2, 4), E(-2, 2), F(3, 2). Draw the image quadrilateral after a rotation of 180° about the point N(2, -2). Label the image quadrilateral C′D′E′F′. D C E F N F′ E′ C′ D′

12. Try This!
Rotate the following right angle triangle 270° counterclockwise about the point (0,0). A B′ A′ B C C′

13. Homework Time!