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Do Now:

Do Now:. 1) Draw a coordinate grid (like below) and label the axes 2)Graph the point (1,2) 3) Reflect (1,2) Over the y axis 4)Write the translation algebraically. Rotations and Dilations. Objective: Rotate and dilate figures in the coordinate plane. Rotation.

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Do Now:

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  1. Do Now: 1) Draw a coordinate grid (like below) and label the axes 2)Graph the point (1,2) 3) Reflect (1,2) Over the y axis 4)Write the translation algebraically

  2. Rotations and Dilations Objective: Rotate and dilate figures in the coordinate plane.

  3. Rotation • A transformation in which a figure is turned about a fixed point, called the center of rotation.

  4. What happens when we rotate a rectangle 90 degrees??

  5. Verbal to algebraic (-2, 3) 90° Counterclockwise Rotation (x, y)  (_________) New coordinates: ( )

  6. Verbal to algebraic (-2, 3) • 180° rotation about the origin (x, y)  (___________)New coordinates: ( )

  7. Verbal to algebraic (-2, 3) 270° Counterclockwise rotation (x, y)  (___________)New coordinates: ( )

  8. Verbal to algebraic (-2, 3) Translation 2 units up and 3 units to the left, followed by a 180° rotation about the origin (x, y)  (___________)New coordinates: ( )

  9. Algebraic to verbal (-2, 3) (x, y)  (-y, x)_______________________ New coordinates: ( ) (x, y) (-X, -Y)__________________________ New coordinates: ( ) (x, y)  (Y, -X)__________________________ New coordinates: ( )

  10. ROTATION RULES 90 degrees counterclockwise around origin:(x, y) (-y, x) 180 degrees around the origin: (x, y)  (-x, -y) 270 degrees counterclockwise around origin: (x, y)  (y, -x)

  11. Scale Factor The scale factor (or scalar factor) measures how much larger or smaller the image is. A transformation that changes the size of the image. Dilation

  12. Steps for Dilations: 1) Multiply both coordinates by a scale factor scale factor: ½ coordinates: -1, -2 (-1(½) ,-2 (½)) 2) Simplify to (-.5, -1) 3) Graph(if required)

  13. Dilations Verbal to algebraic (2, 3) a) Dilated by a scale factor of 3. (x, y)  (___________) New coordinates: ( ) b) Dilated by a scale factor of ½ (x, y)  (___________) New coordinates: ( ) c) Dilated by a scale factor of 1 (x, y)  (___________) New coordinates: ( ) d) Dilated by a scale factor of 2 followed by a 90° rotation (x, y)  (___________) New coordinates: ( )

  14. 4) Algebraic to verbal (2, 3) a) (x, y)  (2x, 2y)__________________________ New coordinates: ( ) b) (x, y)  (1/4x, 1/4y)______________________ New coordinates: ( ) c) (x, y)  (2.5x, 2.5y)_____________________ New coordinates: ( ) d) (x, y)  (-2y, 2x)_______________________ New coordinates: ( )

  15.  1. Point B(s, t) is a vertex of quadrilateral ABCD. What are the coordinates of B’after a 90º counterclockwise rotation? A (-s, -t) B (-t, s) C (t, -s) D (s, t) 

  16. 2. What is the rule for a transformation formed by a translation 3 units to the left and 2 units down followed by a 270º counterclockwise rotation? A [-(x – 3), y – 2] B [y – 2, -(x – 3)] C [-(y – 2), x – 3] D [x – 3, -(y – 2)]

  17. 3. QRS will be dilated by a scale factor of 4, resulting in Q’R’S’. What rule describes this transformation? A (x’, y’) = (¼x, ¼y) B (x’, y’) = (4x, 4y) C (x’, y’) = (x + 4, y + 4) D (x’, y’) = (x – 4, y – 4)

  18. 4. What is the rule for dilation by a scale factor of ½, followed by a 270˚ rotation? A (x’’, y’’) = (2y, -2x) B (x’’, y’’) = (½y, -½x) C (x’’, y’’) = (-½y, ½x) D (x’’, y’’) = (-½x, ½y)

  19. 5. The point P(-3, 2) is dilated by a scale factor of 3. The image P’ of the transformation is then reflected over the x-axis, resulting in point P’’. What are the coordinates of P’’? A (-9, 6) B (-9, -6) C (-6, -4) D (9, -6)

  20. Exit Ticket

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