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Published byHelen Lambert Modified over 3 years ago

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**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.

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**Rotations degrees & direction**

Clockwise

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**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

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**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)

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**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)

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**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)

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**Rotate 90 CW about the Origin (Same as 270 CCW)**

Change the sign of x and switch the order

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Rotate 90 CW

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**Rotate 270 Clockwise (Same as 90 ccw)**

Change the sign of y and switch the order

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**Rotate 90° counterclockwise about the origin**

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**Rotate 90° counterclockwise about the origin**

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**Rotate 180 about the Origin**

ONLY Change the signs

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**Rotate 180° about the origin**

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**Rotate 180° about the origin**

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**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

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**Virtual Nerd Tutoring Lessons**

Lesson on Rotations Lesson on Rotations 90° Lesson on Rotations 180°

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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).

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Lesson 5 Definition of Rotation and Basic Properties

Lesson 5 Definition of Rotation and Basic Properties

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