1. 10.7: Rotations in the Coordinate Plane
Expectation:
G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.
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10.7: Rotations in the Coordinate Plane

2. 10.7: Rotations in the Coordinate Plane
a. Plot A(x, y)
b. Let C be the center of the rotation.
c. Draw CA.
d. Draw CB such that m∠ACB = 
e. Determine A’ on CB such that CA’ = CA.
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10.7: Rotations in the Coordinate Plane

3. 10.7: Rotations in the Coordinate Plane
Draw the preimage and image of A(3,6) under a rotation with magnitude 55° (remember positive degree measure means counterclockwise).
Let the origin be the center of the rotation.
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10.7: Rotations in the Coordinate Plane

4. 10.7: Rotations in the Coordinate Plane
Rotation Equations
R(x,y) = (x’, y’)
x’ = xcos - ysin
y’ = xsin + ycos
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10.7: Rotations in the Coordinate Plane

5. 10.7: Rotations in the Coordinate Plane
Determine P’ = R(P) if P(3,6) and  = 55.
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10.7: Rotations in the Coordinate Plane

6. 10.7: Rotations in the Coordinate Plane
Determine P’ = R(P) if P(-4,8) and  = 57.
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10.7: Rotations in the Coordinate Plane

7. 10.7: Rotations in the Coordinate Plane
A swimmer swims 100 yards due east then 300 yards due north. The current moved her 6 off course from her intended destination. In relation to where she started, where did she end up?
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10.7: Rotations in the Coordinate Plane

8. 10.7: Rotations in the Coordinate Plane
Give (x’,y’) = R(x,y) for each of the following rotations:
a.  = 0
b.  = 90
c.  = 180
d. = 270
e.  = 360
7th hour 4/27/06
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10.7: Rotations in the Coordinate Plane

9. 10.7: Rotations in the Coordinate Plane
Matrices
A matrix is a rectangular arrangement of numbers into rows and columns
The plural of matrix is matrices.
m x n matrix: m rows and n columns
3rd hour 5/1/06
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10.7: Rotations in the Coordinate Plane

10. 10.7: Rotations in the Coordinate Plane
Rotation matrix [ ]
cos  -sin 
sin  cos 
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10.7: Rotations in the Coordinate Plane

11. Rotating (x,y) with magnitude of :[ ]
[ ] x y
cos  -sin 
sin  cos  
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10.7: Rotations in the Coordinate Plane

12. Rotate P(-2,4) by 75 about the origin.
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10.7: Rotations in the Coordinate Plane

13. 10.7: Rotations in the Coordinate Plane
Rotate the triangle with vertices A(1,3), B(4,7) and C(3,-2) 300 about the origin.
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10.7: Rotations in the Coordinate Plane

14. 10.7: Rotations in the Coordinate Plane
Assignment
pages ,
# (odds except 21)
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10.7: Rotations in the Coordinate Plane