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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 Transformations What am I learning today? Rotations What will I do to show that I learned it? Determine coordinates 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 Rotations QUESTION What do I need to know to complete a rotation?

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

6 Course Rotations QUESTION How are objects rotated around the origin on a coordinate plane?

7 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.

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

9 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.

10 Example: Course Rotations Start: A (-4,3) in quadrant II Rotate 270 o clockwise Finish: Quadrant III 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 Rotations x y A B C 3 –3 Graph the pre-image coordinates. 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 Rotations x y A B C 3 –3 C B A Graph the pre-image coordinates. 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. Rotations Around the Origin Course Rotations x y A B C 3 –3 C B A Graph the pre-image coordinates. 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.

14 Course Rotations QUESTION How are the coordinates determined from a rotation around a vertex?

15 Course 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..

16 Triangle ABC has vertices A(-2,0), B(0, 3), C(0, –3). Rotate ABC 90° clockwise about the vertex A. Rotation around a vertex Course Rotations x y B C 3 -2 –3 B C A The pre-image coordinates of triangle ABC are A(-2,0), B(0,3), C(0,-3). The coordinates of the image of triangle ABC are A(-2,0), B(1,-2), C(-5,-2). The corresponding sides, AB and AB make a 90° angle. 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.

17 Triangle ABC has vertices A(-2,0), B(0, 3), C(0, –3). Rotate ABC 180° clockwise about the vertex A. Rotation around a vertex Course Rotations x y B C 3 -2 –3 B C A The pre-image coordinates of triangle ABC are A(-2,0), B(0,3), C(0,-3). The coordinates of the image of triangle ABC are A(-2,0), B(-4,-3), C(-4,3). The corresponding sides, AB and AB make a 180° angle. 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.

18 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?

19 KIM corresponding rotation

20 Practice around Origin 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) Dont forget to note: What quadrant are you starting in?

21 Practice around the Origin P R Q Rotate 90, 180, and 270 degrees counterclockwise

22 Practice around vertex C A C D B A B C D A BC Rotate 90 degrees clockwise Rotate 270 degrees counterclockwise Rotate 180 degrees


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