Transformation: Rotation Unit 4.10 I can perform rotations and identify their transformation notation.

VocabularyVocabulary  Rotation: A transformation where a figure is turned around a fixed point to create a new image.  The lines drawn from the original figure to the center of rotation, and from the center of rotation to the final figure form the angle of rotation.  Example:

Something to Remember: In this Unit, we will only rotate counter clock-wise unless otherwise specified!

Do you know?  80° clock-wise rotation = _______° counter clock-wise rotation?  How do you know?  Answer: The Key: 360°

Try this one!  200° clock-wise rotation = _______° counter clock-wise rotation?  How do you know?  Answer: The Key: 360°

VocabularyVocabulary  Rotation on the Coordinate Plane: To rotate a figure in the coordinate plane, we use the origin as the center of rotation.  Example: Rotate segment AB 180  Example: Rotate segment AB 180° when A(7, 4) and B(6, 1). Find the coordinates of A’ and B’.

  Example: Rotate segment AB 180° when A(7, 4), and B(6, 1). Find the coordinates of A’ and B’. A’ = __________ B’ = ___________ B A

What do you notice about the coordinates? (180°) A(7, 4)  A’(–7, –4) and B(6, 1)  B’(–6, –1) In other words: (x, y)  (–x, –y) Example

Let’s Try Another! Let’s Try Another! Rotate ΔABC 90° when A(6, –1), B(2, –8), and C(1, –1). Find the coordinates of A’, B’ and C’. A’ = __________ B’ = __________ C’ = __________ C B A

What do you notice about the coordinates? (90°) A(6, –1)  A’(1, 6) B(2, –8)  B’(8,2) C(1, –1)  C’(1, 1) In other words: (x, y)  (–y, x) Example

Let’s Try Another! Let’s Try Another! Rotate ΔABCD 270° when A(–4, 5), B(1, 2), C(–6, –2) and D(–8, 3). Find all prime coordinates. Hint: 270° = 90°+180° A’ = __________ B’ = __________ C’ = __________ D’ = __________ B A C D

What do you notice about the coordinates? (270°) A(–4, 5)  A’(5, 4) B(1, 2)  B’(2, –1) C(–6, –2)  C’(–2, 6) D(–8, 3)  D’(3, 8) In other words: (x, y)  (y, –x) Example

A B C A’ B’ C’ Rotate ΔABC counter clock-wise 90°. Label the new image, ΔA’B’C’ and list the coordinates below. A: _____________ B: _____________ C: ____________ A’: ____________ B’: ____________ C’: ____________ (9,-2) (8,-7) (1,-1) (2,9) (7,8) (1,1) 1) 90° Rule: (x,y)  (-y,x)

H I G H’ I’ G’ Rotate ΔGHI 270° counter clock-wise. Label the new image, ΔG’H’I’ and list the coordinates below. G: ____________ H: _____________ I: ______________ G’: ____________ H’: ____________ I’: _____________ (1,5) (7,7) (6,2) (5,-1) (7,-7) (2,-6) 270° Rule: (x,y)  (y,-x) 2)

M N P Rotate polygon MNOP 180° counter clock-wise. Label the new image, M’N’O’P’ and list the coordinates below. M: ____________ N: _____________ O: ____________ P: _____________ M’: ____________ N’: ____________ O’: ____________ P’: ____________ (4,9) (8,5) (1,1) (-4,-9) (-8,-5) (-1,-1) 3) 180° Rule: (x,y)  (-x,-y) O M’ N’ P’ O’ (1,5) (-1,-5)

Homework Time Homework Time Turn It! -- Rotation WS I can perform rotations and identify their transformation notation.