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Coordinate Rules for Rotations

Coordinate Rules for Rotations. Learning Goal 1 (8.G.A.3): Use coordinates to write directions for drawing figures, specify the coordinates of the original and new image under a transformation and specify the coordinate rules for those transformations. A Rotation is….

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Coordinate Rules for Rotations

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  1. Coordinate Rules for Rotations

  2. Learning Goal 1 (8.G.A.3): Use coordinates to write directions for drawing figures, specify the coordinates of the original and new image under a transformation and specify the coordinate rules for those transformations.

  3. A Rotation is… • A rotation is a transformation that turns a figure around a fixed point called the center of rotation. • A rotation is clockwise if its direction is the same as that of a clock hand. • A rotation in the other direction is called counterclockwise. • A complete rotation is 360˚.

  4. Before rotating a figure about the origin on a coordinate grid… • Estimate what quadrant the figure will end up in. • It may help to draw a line from one vertex of the object to the origin. • What quadrant would 90˚ clockwise rotation end up in? • Imagine making a right angle with the line. • It will end up in quadrant 4. • What do you notice about the two triangles?

  5. Before rotating a figure about the origin on a coordinate grid… • Estimate what quadrant the figure will end up in. • It may help to draw a line from one vertex of the object to the origin. • What quadrant would 180˚ counter-clockwise rotation end up in? • Imagine making a straight angle with the line. • It will end up in quadrant 3. • What do you notice about the two triangles?

  6. Goal:accurately rotate an object about the origin and specify the ordered pairs of the new shape. • As we go through the next few examples, try to look for a pattern or relationship between the ordered pairs after each rotation. • Pass out Labsheet 3.3

  7. Rotate points A-E 90˚ counterclockwise about the origin. D’ • Which quadrant will it end up in? • Write a rule for the pattern relating the coordinates of key points to the coordinates of their image after a 90˚ rotation: (x, y) → • Do any points remain unchanged after this rotation? • Do the flag and its image make a symmetric design? C’ E’ B’ (5, 4) (6, 6) (3, 6) A’ (-6, 3) (0, 0) (-4, 5) (-4, 2) (-6, 6) (-y, x)

  8. Rotate points A-E 180˚ counterclockwise about the origin. • Which quadrant will it end up in? • Write a rule for the pattern relating the coordinates of key points to the coordinates of their image after a 180˚ rotation: (x, y) → • Do any points remain unchanged after this rotation? • Do the flag and its image make a symmetric design? (5, 4) (6, 6) (3, 6) (-3, -6) (-6, -6) (0, 0) (-2, -4) (-5, -4) A’ B’ C’ D’ E’ (-x, -y)

  9. When you rotate a figure 180˚, does it matter whether you rotate clockwise or counterclockwise? • Compare Eto E’, D to D’, and Cto C’. What do you notice about each angle pair? • What effect do rotations have on angles? • What effect do rotations have on side lengths? A’ B’ C’ D’ E’

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