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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 and quadrant 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 or point inside the object

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**How do I rotate an object in the coordinate plane?**

Course 2 8-10 Rotations QUESTION How do I rotate an object in the 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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**Start: A (-4,3) in quadrant II Rotate 180o clockwise **

Course 2 8-10 Rotations Start: A (-4,3) in quadrant II Rotate 180o clockwise Finish: In quadrant IV, so 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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**Start: A (-4,3) in quadrant II Rotate 270o clockwise **

Course 2 8-10 Rotations Start: A (-4,3) in quadrant II Rotate 270o clockwise Finish: In quadrant III, so 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. The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3 C’ B’ A’ The coordinates of the image of triangle ABC are A’(0,1), B’(-3,3), C’(0, 5). Remember: A 90 degree rotation x and y change places, then pay attention to the characteristics of the quadrants.

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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. The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3 The coordinates of the image of triangle ABC are A’(-1, 0), B’(-3,-3), C’(-5, 0). C’ B’ A’ Remember: A 180 degree rotation only changes the signs, so pay attention to the characteristics of the quadrants.

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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. The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3 The coordinates of the image of triangle ABC are A’(0,-1), B’(3,-3), C’(0,-5). C’ B’ A’ Remember: A 270 degree rotation x and y change places, then pay attention to the characteristics of the quadrants.

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K I M rotation

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**Practice Rotate P 270o CCW P’(3, -6) Rotate C 90o CW Rotate D 180o CW**

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) D’(1,0) P’(-3,6) C’(2,4) D’(1,0)

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Practice Graph the pre-image, then rotate 90, 180, and 270 degrees counterclockwise P Q R

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Now Try These Graph Triangle MNL with vertices M(0,4), N(3,3), and L(0,0). Rotate 90 degrees clockwise. Graph Triangle ABC with vertices A(-3, -1), B(-3, -2), and C(1, -2). Rotate 90 degrees clockwise.

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Section 12-4. Recall Then you applied these to several oblique triangles and developed the law of sines and the law of cosines.

Section 12-4. Recall Then you applied these to several oblique triangles and developed the law of sines and the law of cosines.

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