10.7: Rotations in the Coordinate Plane

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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. 3/25/2017 10.7: Rotations in the Coordinate Plane

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. 3/25/2017 10.7: Rotations in the Coordinate Plane

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. 3/25/2017 10.7: Rotations in the Coordinate Plane

10.7: Rotations in the Coordinate Plane
Rotation Equations R(x,y) = (x’, y’) x’ = xcos - ysin y’ = xsin + ycos 3/25/2017 10.7: Rotations in the Coordinate Plane

10.7: Rotations in the Coordinate Plane
Determine P’ = R(P) if P(3,6) and  = 55. 3/25/2017 10.7: Rotations in the Coordinate Plane

10.7: Rotations in the Coordinate Plane
Determine P’ = R(P) if P(-4,8) and  = 57. 3/25/2017 10.7: Rotations in the Coordinate Plane

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? 3/25/2017 10.7: Rotations in the Coordinate Plane

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 3/25/2017 10.7: Rotations in the Coordinate Plane

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 3/25/2017 10.7: Rotations in the Coordinate Plane

10.7: Rotations in the Coordinate Plane
Rotation matrix [ ] cos  -sin  sin  cos  3/25/2017 10.7: Rotations in the Coordinate Plane

Rotating (x,y) with magnitude of :
[ ] [ ] x y cos  -sin  sin  cos  3/25/2017 10.7: Rotations in the Coordinate Plane

Rotate P(-2,4) by 75 about the origin.
3/25/2017 10.7: Rotations in the Coordinate Plane

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. 3/25/2017 10.7: Rotations in the Coordinate Plane

10.7: Rotations in the Coordinate Plane
Assignment pages , # (odds except 21) 3/25/2017 10.7: Rotations in the Coordinate Plane

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