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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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Course 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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A full turn is a 360° rotation. 90 ° 180° 360° How do you determine the angle of rotation? What are they rotating around? 270° A quarter turn is a 90° rotation. A half turn is a 180° rotation. A three quarter turn is a 270° rotation.

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Course Rotations QUESTION What do I need to know to complete a rotation?

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

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Course Rotations QUESTION How do I rotate an object in the coordinate plane?

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Course Rotations To Rotate 180 o 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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Course Rotations Start: A (-4,3) in quadrant II Rotate 180 o clockwise Finish: In quadrant IV, so x is positive and y is negative. A’ (4,-3)

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

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Course Rotations Start: A (-4,3) in quadrant II Rotate 270 o clockwise Finish: In quadrant III, so x is negative and y is negative. A’ (-3,-4)

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Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 90° counterclockwise about the origin. Rotations Around the Origin Course Rotations x y A B C 3 –3 The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). 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. C’ B’ A’

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

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

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KIM rotation

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Practice Using these three points: P(6,3); C(-2,- 4); D(-1,0) Rotate P 270 o CCW Rotate C 90 o CW Rotate D 180 o CW Rotate P 270 o CW Rotate C 180 o CCW Rotate D 90 o CW P’(3, -6) C’(-4,2) D’(1,0) P’(-3,6) C’(2,4) D’(1,0)

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

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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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