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## Rotations

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**Rotations**A turn around a center. The distance from the center to any point on the shape stays the same.**Rotations degrees & direction**Clockwise**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**Rotate ∆TSN 90°cw**(x, y) (y, -x) T’ T(-1, 1) T'(1, 1) S(4, -1) S'(-1, -4) N(1, -4) N'(-4, -1) N’ S’ (270 ° CCW rotation)**Rotate ∆TSN 180°**(x, y) (-x, -y) T(-1, 1) T'(1, -1)S(4, -1) S'(-4, 1)N(1, -4) N'(-1, 4)**Rotate ∆TSN270° cw**(x, y) to (-y, x) T(-1, 1) T'(-1, -1)S(4, -1) S'(1, 4)N(1, -4) N'(4, 1)**Rotate 90 CW about the Origin(Same as 270 CCW)**Change the sign of x and switch the order**Rotate 270Clockwise(Same as 90ccw)**Change the sign of y and switch the order**Rotate 180about the Origin**ONLY Change the signs**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**Virtual Nerd Tutoring Lessons**Lesson on Rotations http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/define-transformations/rotation-definition Lesson on Rotations 90° http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/rotating-figures/rotate-90-degrees-about-origin Lesson on Rotations 180° http://www.virtualnerd.com/pre-algebra/geometry/transformations-symmetry/rotating-figures/rotate-180-degrees-about-origin**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 900(x, y) (y, -x). • For a rotation of 1800(x,y) (-x, -y). • For a rotation of 2700(x,y) (-y, x). • When a point (x, y) is rotated counterclockwise about the origin, the following rules are true: • For a rotation of 900 (x,y) (-y, x). • For a rotation of 1800(x,y) (-x, -y). • For a rotation of 2700 (x, y) (y, -x).