Graphing Transformations 3
description
Transcript of Graphing Transformations 3
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Graphing Transformations 3
Rotation – the motion of an object around a fixed point
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Direction of rotation – can be clockwise or counter-clockwise
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Centre of rotation – the fixed point around which the rotation takes place
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Angle of rotation – the amount of rotation made
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360°
centre of rotation
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90°
270°
counter-clockwise
clockwise-270°
+90°
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180° counter-clockwise
180° clockwise-180°
+180°
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A rotation +90°
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A rotation +180°
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A rotation +270°
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Would the images be different if the figures had been rotated clockwise instead of counter-clockwise?
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A rotation -90°
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Would the images be different if the figures had been rotated clockwise instead of counter-clockwise?
A 90° clockwise rotation produces the same image as a 270° counter-clockwise rotation, and vice versa.
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Coordinates
A
B
C
DA’
B’
C’
D’A(0,1)B(2,3)C(4,2)D(3,0)1
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A’(-1,0)B’(-3,2)C’(-2,4)D’(0,3)
A rotation +90° OR -270°
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What patterns do you see in the coordinates of the figure and its image?
• x-coordinates and y-coordinates switched and the x-coordinates have the opposite sign
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Coordinates
A
B
C
D
A’
B’
C’
D’
A(0,1)B(2,3)C(4,2)D(3,0)1
4-4 1 2 3
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y
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A’(0,-1)B’(-2,-3)C’(-4,-2)D’(-3,0)
A rotation +180° OR -180°
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What patterns do you see in the coordinates of the figure and its image?
• x-coordinates and y-coordinates have the opposite sign
![Page 20: Graphing Transformations 3](https://reader035.fdocuments.us/reader035/viewer/2022062323/568161d9550346895dd1e20f/html5/thumbnails/20.jpg)
Coordinates
A
B
C
D
A’
B’
C’
D’
A(0,1)B(2,3)C(4,2)D(3,0)1
4-4 1 2 3
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-3 -1-2
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A’(1,0)B’(3,-2)C’(2,-4)D’(0,-3)
A rotation +270° OR -90°
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What patterns do you see in the coordinates of the figure and its image?
• x-coordinates and y-coordinates switched and the y-coordinates have the opposite sign
![Page 22: Graphing Transformations 3](https://reader035.fdocuments.us/reader035/viewer/2022062323/568161d9550346895dd1e20f/html5/thumbnails/22.jpg)
How are a figure and its rotation image alike?• They are congruent. • They have the same orientation. If ABCD is read clockwise, then A’B’C’D’ is read clockwise.
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Rotate ABCD -90°
Coordinates
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Rotate ABCD +270°
Coordinates
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Rotate ABCD 180°
Coordinates
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Coordinates
A
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C
D
A(0,1)B(2,3)C(4,2)D(3,0)1
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A rotation