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Rotations A turn around a center. The distance from the center to any point on the shape stays the same.

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Presentation on theme: "Rotations A turn around a center. The distance from the center to any point on the shape stays the same."— Presentation transcript:

1 Rotations A turn around a center. The distance from the center to any point on the shape stays the same.

2 Clockwise Rotations  degrees & direction

3 Rotation of 90°: Rotation of 180°: Rotation of 270°: A rotation turns a figure through an angle about a fixed point called the center. It is a rigid isometry. Rules of rotation are for clockwise rotations. Counter clockwise rotations are opposite clockwise. 90°cw = 270°ccw and 270°cw = 90°ccw

4 N(1, -4)  N'(-4, -1) (270 ° CCW rotation) T’ N’ S’ Rotate ∆TSN 90°cw (x, y)  (y, -x) T(-1, 1)  T'(1, 1) S(4, -1)  S'(-1, -4)

5 T(-1, 1)  T'(1, -1) S(4, -1)  S'(-4, 1) N(1, -4)  N'(-1, 4) Rotate ∆TSN 180° (x, y)  (-x, -y)

6 T(-1, 1)  T'(-1, -1) S(4, -1)  S'(1, 4) N(1, -4)  N'(4, 1) Rotate ∆TSN 270° cw (x, y) to (-y, x)

7 Rotate 90  CW about the Origin (Same as 270  CCW) Change the sign of x and switch the order

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9 Rotate 90  CW

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11 Rotate 270  Clockwise (Same as 90  ccw) Change the sign of y and switch the order

12 Rotate 90° counterclockwise about the origin

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14 Rotate 180  about the Origin ONLY Change the signs

15 Rotate 180° about the origin

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17 Rotation of 90°: Rotation of 180°: Rotation of 270°: A rotation turns a figure through an angle about a fixed point called the center. It is a rigid isometry. Rules of rotation are for clockwise rotations. Counter clockwise rotations are opposite clockwise. 90°cw = 270°ccw and 270°cw = 90°ccw

18 Virtual Nerd Tutoring Lessons algebra/geometry/transformations-symmetry/define- transformations/rotation-definition Lesson on Rotations algebra/geometry/transformations- symmetry/rotating-figures/rotate-90- degrees-about-origin Lesson on Rotations 90° algebra/geometry/transformations- symmetry/rotating-figures/rotate-180- degrees-about-origin Lesson on Rotations 180°

19 Coordinate Rules for Rotations about the origin: When a point (x, y) is rotated clockwise about the origin, the following rules are true: For a rotation of 90 0 (x, y)  (y, -x). For a rotation of (x,y)  (-x, -y). For a rotation of (x,y)  (-y, x). When a point (x, y) is rotated counterclockwise about the origin, the following rules are true: For a rotation of 90 0 (x,y)  (-y, x). For a rotation of (x,y)  (-x, -y). For a rotation of (x, y)  (y, -x).


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