2.3 – Perform Rotations

Rotation: Transformation that turns a figure about a fixed point

Center of Rotation:

The point that the rotation happens around

Angle of Rotation:

How many degrees clockwise or counterclockwise a shape is turned

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:

'Q

• If Q is not the center of rotation, then and 'QP Q P 'm QPQ x

x°

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:

'Q

• If Q is the center of rotation, then 'Q Q

Q 'Q

Example #1: ROTATIONS ON A GRID Consider what you know about rotation, a motion that turns a shape about a point. Does it make any difference if a rotation is clockwise ( ) versus counterclockwise ( )? If so, when does it matter? Are there any circumstances when it does not matter? And are there any situations when the rotated image lies exactly on theoriginal shape?

Investigate these questions as you rotate the shapes below about the given point below. Use tracing paper if needed. Be prepared to share your answers to the questions posed above.

- 180° doesn’t matter if you go clockwise or counterclockwise

- 90° counterclockwise is the same as 270 clockwise

- 360° rotates all the way around and matches the original shape

Example #2: Rotate the triangle in the given degree about the origin.

(2,2)'A

(5,5)'B

(5,2)

'C

(2,2)'A

(5,5)

'B

(5,2)

'C

180

(2,2)'A

(5,5)

'B

(5,2)

'C

270

Example #3: State if the rotation about the origin is 90°, 180°, or 270° counter-clockwise.

4. Find the value of each variable in the rotation.

x = 4

z = 3

y = z + 2y = 3 + 2y = 5

4. Find the value of each variable in the rotation.

4s = 24s = 6

r = 2s – 3 r = 2(6) – 3

r = 9

r = 12 – 3