Transformations

1. 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°) • Rotation by 270° about the origin: R(origin, 270°)

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!!!!