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Transformations Review

Transformations Review. Recall: Types of Transformations. Translations Reflections Rotations. glide. FLIP. Turn. Recall: Notation. When you name an image, take the corresponding point of the preimage and add a prime symbol, like this:. A. B. A’. B’. C. D. C’. D’.

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Transformations Review

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  1. Transformations Review

  2. Recall: Types of Transformations • Translations • Reflections • Rotations glide FLIP Turn

  3. Recall: Notation • When you name an image, take the corresponding point of the preimage and add a prime symbol, like this: A B A’ B’ C D C’ D’

  4. Translation Rules What would each of the following rules do to the preimage? • (x, y) → (x + 5, y) • (x, y) → (x, y - 3) • (x, y) → (x - 2, y) • (x, y) → (x, y + 1) • (x, y) → (x + 7, y - 2) • MOVE RIGHT 5 UNITS • MOVE DOWN 3 UNITS • MOVE LEFT 2 UNITS • MOVE UP 1 UNIT • MOVE RIGHT 7, DOWN 2

  5. Translation Example • Find the image of triangle XYZ with vertices X(5, 1), Y(-1, 4), and Z(1, 7) for the translation (x, y) → (x + 4, y - 6).

  6. Translation Practice • Find the image of triangle DEF with vertices D(-2, 4), E(-2, -3), and F(5, 0) for the translation (x, y) → (x + 5, y + 3).

  7. Reflection Rules • What happens when we reflect a figure over the x axis? (x, y) → (x, -y) • What happens when we reflect a figure over the y axis? (x, y) → (-x, y)

  8. Reflection Example • Reflect triangle ABC with vertices A(-4, -3), B(0, -3), and C(4, 2) across the x axis.

  9. Reflection Practice • Reflect triangle ABC with vertices A(-4, -3), B(0, -3), and C(4, 2) across the y axis.

  10. Rotation Rules • What is the rule to rotate a figure 90° about the origin? (x, y) → (-y, x) • What is the rule to rotate a figure 180° about the origin? (x, y) → (-x, -y) • What is the rule to rotate a figure 270° about the origin? (x, y) → (y, -x)

  11. Rotation Example • Find the image of quadrilateral WXYZ with vertices W(3, 2), X(6, 3), Y(2, -2), and Z(5, -2) for the 180° counterclockwise rotation about the origin.

  12. Rotation Practice • Find the image of quadrilateral WXYZ with vertices W(3, 2), X(6, 3), Y(2, -2), and Z(5, -2) for the 90° rotation counterclockwise about the origin.

  13. Mixed Review Describe the result of applying each rule below to a figure in the coordinate plane. • A(x, y) = (x + 4, y) • S(x, y) = (x, -y) • T(x, y) = (x, y - 3) • G(x, y) = (x - 2, y + 5) • R(x, y) = (-y, x) • M(x, y) = (-x, y) • Translation RIGHT 4 • Reflection over x axis • Translation DOWN 3 • Translation LEFT 2, UP 5 • Rotation 90° about origin • Reflection over y axis

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