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Honors Geometry Transformations Section 2 Rotations

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A rotation is a transformation in which every point is rotated the same angle measure around a fixed point. The fixed point is called the center of rotation.

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The ray drawn from the center of rotation to a point and the ray drawn from the center of rotation to the point’s image form an angle called the angle of rotation.

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Rotations can be clockwise ( ) or counterclockwise ( ).

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Let’s take a look at rotations in the coordinate plane.

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Example 1: Rotate 180 clockwise about the origin (0, 0). Give the coordinates of _______ _______

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Would the coordinates of and be different if we had rotated counterclockwise instead? NO

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Rotations around the origin can be made very easily by simply rotating your paper the required angle measure. Note: The horizontal axis is always the x-axis and the vertical axis is always the y-axis.

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Example 2: Rotate 90 clockwise about the origin. Give the coordinates of ________ ________

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A B

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Example 3: Rotate 90 counterclockwise about the origin. Give the coordinates of ________ ________ A B

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For rotations of 90 0 around a point other than the origin, we must work with the slopes of the rays forming the angle of rotation. Remember: If two rays are perpendicular then their slopes are opposite reciprocals.

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Example 4: Rotate 90 clockwise about the point (–1, 3).

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Example 4: Rotate 90 counterclockwise about the point (–1, 3).

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Example 6: Rotate 90 0 counterclockwise around the point (3, 0)

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A figure has rotational symmetry if it can be rotated through an angle of less than 360 and match up with itself exactly.

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Example 7: State the rotational symmetries of a square regular pentagon

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Example 8: Name two capital letters that have 180 rotational symmetry.

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