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1/15/201410.7: Rotations in the Coordinate Plane Expectation: G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image.

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Presentation on theme: "1/15/201410.7: Rotations in the Coordinate Plane Expectation: G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image."— Presentation transcript:

1 1/15/ : 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.

2 1/15/ : 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 1/15/ : 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.

4 1/15/ : Rotations in the Coordinate Plane Rotation Equations R(x,y) = (x, y) x = xcos - ysin y = xsin + ycos

5 1/15/ : Rotations in the Coordinate Plane Determine P = R(P) if P(3,6) and = 55.

6 1/15/ : Rotations in the Coordinate Plane Determine P = R(P) if P(-4,8) and = 57.

7 1/15/ : 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?

8 1/15/ : 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

9 1/15/ : 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

10 1/15/ : Rotations in the Coordinate Plane Rotation matrix cos -sin sin cos [ ]

11 1/15/ : Rotations in the Coordinate Plane Rotating (x,y) with magnitude of : cos -sin sin cos [] [][] xyxy

12 1/15/ : Rotations in the Coordinate Plane Rotate P(-2,4) by 75 about the origin.

13 1/15/ : Rotations in the Coordinate Plane Rotate the triangle with vertices A(1,3), B(4,7) and C(3,-2) 300 about the origin.

14 1/15/ : Rotations in the Coordinate Plane Assignment pages , # (odds except 21)


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