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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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Presentation on theme: "What is similar about these objects? What do we need to pay attention to when objects are rotated?"— Presentation transcript:

1 What is similar about these objects? What do we need to pay attention to when objects are rotated?

2 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.

3 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.

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

5 To rotate: Course 2 8-10 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

6 Course 2 8-10 Rotations QUESTION How do I rotate an object in the coordinate plane?

7 Course 2 8-10 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.

8 Course 2 8-10 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)

9 Course 2 8-10 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.

10 Course 2 8-10 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)

11 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 2 8-10 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’

12 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 2 8-10 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.

13 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 2 8-10 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’

14 KIM rotation

15 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)

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

17 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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