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

Rotations  degrees & direction Clockwise

𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙) 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. Rotation of 90°:     Rotation of 180°:    Rotation of 270°:      𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙) Counter clockwise rotations are opposite clockwise. 90°cw = 270°ccw and 270°cw = 90°ccw

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

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) T(-1, 1)  T'(1, -1) S(4, -1)  S'(-4, 1) N(1, -4)  N'(-1, 4)

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) 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 90 CW

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

Rotate 90° counterclockwise about the origin

Rotate 90° counterclockwise about the origin

Rotate 180 about the Origin ONLY Change the signs

Rotate 180° about the origin

Rotate 180° about the origin

𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙) 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. Rotation of 90°:     Rotation of 180°:    Rotation of 270°:      𝑹 𝟗𝟎°𝒄𝒘 𝒙, 𝒚 =(𝒚, −𝒙) 𝑹 𝟏𝟖𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒙, −𝒚) 𝑹 𝟐𝟕𝟎°𝒄𝒘 𝒙, 𝒚 =(−𝒚, 𝒙) 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 2700 (x, y)  (y, -x).