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Rotations on the Coordinate Plane

Rotations on the Coordinate Plane. Rotations on the Coordinate Plane. Rotations move an object about a central point Windmill vanes rotate around a central arm as do the hands of a clock. Rotations on the Coordinate Plane. On the coordinate plane, the central point of rotation is the origin.

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Rotations on the Coordinate Plane

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  1. Rotations on the Coordinate Plane

  2. Rotations on the Coordinate Plane • Rotations move an object about a central point • Windmill vanes rotate around a central arm as do the hands of a clock

  3. Rotations on the Coordinate Plane • On the coordinate plane, the central point of rotation is the origin

  4. Rotations Mini-Lab • The graph models vanes of a Dutch windmill • What are the measurements of angle COG, angle GOK, angle KOP, and angle POC? They each measure 90º F G E H C B D A I L J K Q M P N

  5. Rotations Mini-Lab • Record the coordinates of each lettered point below: F G E H E (0, 2) F (-4, 6) G (-5, 5) H (-1, 1) I (-2, 0) J (-6, -4) K (-5, -5) L (-1, -1) A (2, 0) B (6, 4) C (5, 5) D (1, 1) M (0, -2) N (4, -6) P (5, -5) Q (1, -1) C B D A I L J K Q M P N

  6. Rotations Mini-Lab • As the windmill turns, each point of one vane will occupy the previous location of the corresponding point on another vane. F G E H C B D A I L J K Q M P N

  7. Rotations Mini-Lab • Compare the coordinates of the vertices of vane ABCD with those of vane EFGH • What do you notice? F G E H They are switched and then the x-coordinate of each point is multiplied by -1. C B D A A (2, 0) E (0, 2) B (6, 4) F (-4, 6) C (5, 5) G (-5, 5) D (1, 1) H (-1, 1) I L J K Q M P N

  8. Rotations Mini-Lab • How many degrees did the vane rotate to move from point C to point G? 90º F G E H C B D A I L J K Q M P N

  9. Rotations Mini-Lab • Compare the coordinates of the vertices of vane ABCD with those of vane IJKL • What do you notice? Both coordinates of each point are multiplied by -1 F G E H C B D A A (2, 0) I (-2, 0) B (6, 4) J (-6, -4) C (5, 5) K (-5, -5) D (1, 1) L (-1, -1) I L J K Q M P N

  10. Rotations Mini-Lab • How many degrees did the vane rotate to move from point C to point K? 180º F G E H C B D A I L J K Q M P N

  11. Rotations Mini-Lab What did we learn? • To rotate a figure 90º counterclockwise, switch the coordinates of each point and then multiply the x-coordinate by -1 • To rotate a figure 180º, multiply both coordinates of each point by -1

  12. Rotations Checkpoint • Triangle ABC has vertices A (1, 3), B (6, 7), and C (9, 1). • Rotate the triangle ABC 90º counterclockwise and give the vertices of triangle A’B’C’ A’ (-3, 1) B’ (-7, 6) C’ (-1, 9)

  13. Rotations Checkpoint • Triangle ABC has vertices A (1, 3), B (6, 7), and C (9, 1). • Rotate the triangle ABC 180ºand give the vertices of triangle A’B’C’ A’ (-1, -3) B’ (-6, -7) C’ (-9, -1)

  14. Homework • Practice Worksheet 11-10 • Practice Skills 6-9 • DUE TOMORROW!!

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