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Coordinate Rules for Rotations

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43210 In addition to 3, I am able to go above and beyond by applying what I know about coordinate rules for performing transformations and could teach someone else. 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. I can use coordinates for drawing figures. I can specify coordinates of the new image after the transformation. I can specify the rules for the transformations. I have partial understanding of how to 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. With help I may have a partial understanding of how to use coordinates to write directions for drawing figures and specify the coordinates of the original and new image under a transformation. Even with help, I am not able to use coordinates to write directions for drawing figures nor specify the coordinates of the original and new image under a transformation. 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.

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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˚.

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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?

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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?

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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

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Rotate points A-E 90˚ 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 90˚ 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) (0, 0) (-4, 2 ) (-4, 5 ) (-6, 6) (-6, 3) (-y, x) B’ C’ D’ E’ A’

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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) (0, 0) (-2, -4 ) (-5, -4) (-6, -6) (-3, -6) (-x, -y) B’ C’ D’ E’ A’

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

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