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**What is similar about these objects?**

What do we need to pay attention to when objects are rotated?

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**What am I learning today? What will I do to show that I learned it?**

Course 2 8-10 Transformations What am I learning today? Rotations What will I do to show that I learned it? Determine coordinates resulting from a rotation.

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**How do you determine the angle of rotation?**

A full turn is a 360° rotation. A quarter turn is a 90° rotation. 360° 90° A half turn is a 180° rotation. 180° 270° A three quarter turn is a 270° rotation. What are they rotating around?

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**What do I need to know to complete a rotation?**

Course 2 8-10 Rotations QUESTION What do I need to know to complete a rotation?

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**To rotate: - the direction – CW or CCW - the degrees – 90o, 180o, 270o**

Course 2 8-10 Rotations To rotate: - the direction – CW or CCW - the degrees – 90o, 180o, 270o - the center or point of rotation – origin, vertex, or point inside the object

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**How are objects rotated around the origin on a coordinate plane?**

Course 2 8-10 Rotations QUESTION How are objects rotated around the origin on a coordinate plane?

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**To Rotate 180o around origin: 1. Keep your x- and y-values the same. **

Course 2 8-10 Rotations To Rotate 180o around origin: 1. Keep your x- and y-values the same. . 2. Move to the opposite quadrant. I to III III to I II to IV IV to II 3. Put the appropriate signs based on the quadrant.

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**Example: Start: A (-4,3) in quadrant II Rotate 180o clockwise**

Course 2 8-10 Rotations Example: Start: A (-4,3) in quadrant II Rotate 180o clockwise Finish: Quadrant IV x is positive and y is negative. A’ (4,-3)

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**To Rotate 90o or 270o around origin: 1. x- and y-value switch places. **

Course 2 8-10 Rotations To Rotate 90o or 270o around origin: 1. x- and y-value switch places. x becomes y and y becomes x. . 2. Find the quadrant. Move one for 90o or three for 270o. Pay attention to the direction. 3. Put the appropriate signs based on the quadrant.

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**Example: Start: A (-4,3) in quadrant II Rotate 270o clockwise**

Course 2 8-10 Rotations Example: Start: A (-4,3) in quadrant II Rotate 270o clockwise Finish: Quadrant III x is negative and y is negative. A’ (-3,-4)

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**Rotations 8-10 Rotations Around the Origin**

Course 2 8-10 Rotations Rotations Around the Origin Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 90° counterclockwise about the origin. x y A B C 3 –3 Graph the pre-image coordinates. C’ B’ A’ Remember: A 90 degree rotation x and y change places, then pay attention to the characteristics of the quadrants. The coordinates of the image of triangle A’B’C’ are A’(0, 1), B’(-3,3), C (0.5).

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**Rotations 8-10 Rotations Around the Origin**

Course 2 8-10 Rotations Rotations Around the Origin Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° counterclockwise about the origin. x y A B C 3 –3 Graph the pre-image coordinates. Remember: A 180 degree rotation only changes the signs, so pay attention to the characteristics of the quadrants. C’ B’ A’ The coordinates of the image of triangle ABC are A’(-1, 0), B’(-3,-3), C’(-5, 0).

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**Rotations 8-10 Rotations Around the Origin**

Course 2 8-10 Rotations Rotations Around the Origin Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 270° counterclockwise about the origin. x y A B C 3 –3 Graph the pre-image coordinates. Remember: A 270 degree rotation x and y change places, then pay attention to the characteristics of the quadrants. The coordinates of the image of triangle A’B’C’ are A’(0,-1), B’(3,-3), C’(0,-5). C’ B’ A’

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**How are the coordinates determined from a rotation around a vertex?**

Course 2 8-10 Rotations QUESTION How are the coordinates determined from a rotation around a vertex?

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**To Rotate around a vertex: **

Course 2 8-10 Rotations To Rotate around a vertex: 1. Coordinates of the center of rotation stay the same. 2. Corresponding sides create an angle equal to the degree of rotation 3. Each vertex in the shape must stay an equal distance from the center of rotation..

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**Rotations 8-10 Rotation around a vertex**

Course 2 8-10 Rotations Rotation around a vertex Triangle ABC has vertices A(-2,0), B(0, 3), C(0, –3). Rotate ∆ABC 90° clockwise about the vertex A. The pre-image coordinates of triangle ABC are A(-2,0), B(0,3), C(0,-3). x y The coordinates of the image of triangle ABC are A’(-2,0), B’(1,-2), C’(-5,-2). B 3 B’ C’ The corresponding sides, AB and AB’ make a 90° angle. A -2 Notice that vertex B is 2 units to the right and 3 units above vertex A, and vertex B’ is 3 units to the right and 2 units to the below vertex A. –3 C

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**Rotations 8-10 Rotation around a vertex**

Course 2 8-10 Rotations Rotation around a vertex Triangle ABC has vertices A(-2,0), B(0, 3), C(0, –3). Rotate ∆ABC 180° clockwise about the vertex A. The pre-image coordinates of triangle ABC are A(-2,0), B(0,3), C(0,-3). x y The coordinates of the image of triangle ABC are A’(-2,0), B’(-4,-3), C’(-4,3). B B’ C’ 3 A The corresponding sides, AB and AB’ make a 180° angle. -2 Notice that vertex B is 2 units to the right and 3 units above vertex A, and vertex B’ is 2 units to the left and 3 units below vertex A. –3 C

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**Where is the point of rotation?**

A point OUTSIDE the shape A point INSIDE the Shape How are these rotations similar? How are these rotations different?

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K I M corresponding rotation

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**Practice around Origin**

Using these three points: P(6,3); C(-2,- 4); D(-1,0) Rotate P 270o CCW Rotate C 90o CW Rotate D 180o CW Rotate P 270o CW Rotate C 180o CCW Rotate D 90o CW P’(3, -6) C’(-4,2) Don’t forget to note: What quadrant are you starting in? D’(1,0) P’(-3,6) C’(2,4) D’(1,0)

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**Practice around the Origin**

Rotate 90, 180, and 270 degrees counterclockwise P Q R

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**Practice around vertex C**

Rotate 90 degrees clockwise A B D C D A B A C B Rotate 180 degrees C Rotate 270 degrees counterclockwise

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Algebraic Representations of Transformations Day 2

Algebraic Representations of Transformations Day 2

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