1. Goal: to rotate a figure around a central point
Transformations
Goal: to rotate a figure around a central point

2. Transformations and rotations
Transformation refers to any copy of a geometric figure, similar to copying and pasting on your computer.
A Rotation is a type of transformation where the geometric figure is spun around a fixed point known as the “center of rotation”.
Rotations can be made “clockwise” and “counterclockwise”.
Common rotations are 45, 90, 180, and 270 degrees.
Rotation A to A’ 90 degrees counter clockwise

3. Rotation by 180° about the origin: R(origin, 180°)

4. Graphing Rotations
The easiest way to think about rotations is to first think of a single coordinate rotation.
1. Graph the point (1,2) on your paper.
2. Rotate this point 90 degrees clockwise by first drawing a straight line to the “origin”.
3. Secondly, draw a straight line from the origin down and to the right in order to form a right angle.
4. Your second point should fall at (2,-1).

5. 180-degree rotation
1. From the same point (1,2), draw a straight line through the origin.
2. The point that your line hits that is equidistance from (1,2) is your 180-degree clockwise rotation.
3. Your second point should fall at (-1,-2)

6. 270-degree rotation
1. Start from (1,2), draw a straight line through the origin until you hit (-1,-2).
2. This is 180 degrees from the last example.
3. We must add 90 degrees to this.
4. Draw another line from the origin up and to the left to make a 90-degree angle between (-1,-2), the origin, and a last point.
5. This point should fall on (-2,1).

7. RULE: A rotated object’s vertices will form an angle with its original object’s vertices equal to the degree measure of the rotation.
The above rotation shows 90-degree angles between all rotated vertices.

8. Example 2: 180-degree rotation
All of the vertices of the triangle on the left are rotated 180 degrees through the center of reflection.

9. Practice!!!!