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2.3 – Perform Rotations

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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

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A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that: If Q is not the center of rotation, then and x°x°

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

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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 the original shape?

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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.

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- 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

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

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(2,2) (5,5) (5,2)

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(2,2) (5,5) (5,2)

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(2,2) (5,5) (5,2)

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

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4. Find the value of each variable in the rotation. x = 4 z =3 y = z + 2 y = y = 5

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4. Find the value of each variable in the rotation. 4s = 24 s = 6 r = 2s – 3 r = 2(6) – 3 r = 9 r = 12 – 3

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