1. To rotate a figure:
Draw a segment connecting a vertex (we will call
point A) of the figure and the center of rotation We will
call Point P).
Using a protractor and segment AP as one side of an angle, measure the degree of rotation in the direction indicated (clockwise or counterclockwise)and draw a ray for the other side of the angle.
Use a compass or ruler to measure the length of
segment AP. Then, use the compass or ruler to mark
the same distance on the new ray drawn in step 2. This
marking (point) will be the new image’s vertex A’
Repeat for each vertex in the figure, draw segments connecting the new images vertices.

2. To see an example, look on page 413 of the online text
To see an example, look on page 413 of the online text. Once you click the link, you will need to:
Login using username “mathbooks” and password “mathbooks”
Click the “geometry” text book
Type 413 in the “jump to page” window at top of the page

3. Lessons 13.6: Rotations
Transformations:
1) Translation
2) Reflection
3) Rotation
Rotation: a “turning” move - geometric figure is turned about a fixed point called the center of rotation
Angle of Rotation: Formed by rays drawn from the center of rotation to a point on the figure and to the corresponding point on the new image.
Isometry: A transformation that preserves (keeps the same) lengths
*** Rotations, reflections, and translations are isometric

4. Example of Rotation – Rotate 90 clockwise about the originA B’ A’ B C C’
A’ (6, 5)
B’ (1, 5)
C’ (1, 2)

5. Example of Rotation – Rotate 90 counterclockwise about the originA B C
A’ (-6, -5)
B’ (-1, -5)
C’ (-1, -2 C’ A’ B’

6. Example of Rotation – Rotate 180 clockwise about the originA B C B’
A’ (5, -6)
B’ (5, -1)
C’ (2, -1 C’ A’

7. Example of Rotation – Rotate 180 counterclockwise about the originA B C B’
A’ 5, -6)
B’ (5, -1)
C’ (2, -1 C’ A’

8. Rotating about the origin
Rotate 90 Clockwise
Rotate 90 Counterclockwise:
Rotate 180 Clockwise or Counterclockwise:
Switch x and y coordinates, multiply new y-coord. by -1
(x, y)  (y, -x)
Switch x and y coordinates, multiply new x-coord. by -1
(x, y)  (-y, x)
Multiply both x and y by -1 (NO switching of coordinates)
(x, y)  (-x, -y)

9. Does the following figure have rotational symmetry?
A figure has Rotational Symmetry if a rotation of 180 or less clockwise (or counterclockwise) about its center produces an image that fits exactly on the original figure. (turn paper to see if rotational symmetry)
Example :
Does the following figure have rotational symmetry?
                          
                           
                          
Rotate 90° counterclockwise
Rotate 90°
Rotate 180°
Has rotational symmetry for rotating clockwise or counterclockwise 90° or 180° .

10. Examples: State whether the figure does or does not have rotational symmetry
1) )
3) ) NO
YES NO
YES