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Lesson 9-2 Translations

Lesson 9-2 Translations. Translation- transformation that moves all the points in a figure the same distance in the same direction. . Example 2-1a.

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Lesson 9-2 Translations

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  1. Lesson 9-2 Translations • Translation- transformation that moves all the points in a figure the same distance in the same direction.

  2. Example 2-1a COORDINATE GEOMETRYParallelogram TUVW has vertices T(–1, 4),U(2, 5),V(4, 3), and W(1, 2). Graph TUVW and its image for the translation (x, y)  (x – 4, y – 5). This translation moved every point of the preimage 4 units left and 5 units down. T(–1, 4) T' (–1 – 4, 4 – 5) or T' (–5, –1)U(2, 5) U' (2 – 4, 5 – 5) or U' (–2, 0)V(4, 3) V' (4 – 4, 3 – 5) or V' (0, –2)W(1, 2) W' (1 – 4, 2 – 5) or W' (–3, –3) Plot the translated vertices and connect to form parallelogram T'U'V'W'.

  3. Example 2-1a Answer:

  4. Example 2-1b COORDINATE GEOMETRYParallelogramLMNPhas verticesL(–1, 2),M(1, 4),N(3, 2), andP(1, 0).GraphLMNPand its image for the translation(x, y)  (x + 3, y – 4). Answer:

  5. Example 2-2a ANIMATIONThe graph shows repeated translations that result in the animation of a raindrop. Find the translation that moves raindrop 2 to raindrop 3 and then the translation that moves raindrop 3 to raindrop 4.

  6. Example 2-2a To find the translation from raindrop 2 to raindrop 3, use the coordinates at the top of each raindrop. Use the coordinates (1, 2) and (–1, –1) in the formula. Subtract 1 from each side. Subtract 2 from each side.

  7. (x, y) (–1, –1) (–1, –4) Example 2-2a The translation is (x – 2, y – 3) from raindrop 2 to raindrop 3. Use the coordinates (–1, –1) and (–1, –4) to find the translation from raindrop 3 to raindrop 4. Add 1 to each side. Add 1 to each side.

  8. The translation is from raindrop 3 to raindrop 4. Answer: Example 2-2a

  9. Example 2-2b ANIMATION The graph shows repeated translations that result in the animation of a lightning bolt. Find the translation that moves lightning bolt 3 to lightning bolt 4 and then the translation that moves lightning bolt 2 to lightning bolt 1. Answer: (x – 3, y – 1); (x + 2, y + 2)

  10. Example 2-3a In the figure, lines p and q are parallel. Determine whether the pink figure is a translation image of the blue preimage, quadrilateral EFGH.

  11. Example 2-3a Reflect quadrilateral EFGH in line p. The result is the green image, quadrilateral E'F'G'H'. This is not a reflection of quadrilateral EFGH in line p, so quadrilateral E'F'G'H' is not a translation of quadrilateral EFGH. Answer: Quadrilateral E''F''G''H'' is not a translation image of quadrilateral EFGH.

  12. Example 2-3b In the figure, lines n and m are parallel. Determine whether A''B''C''is a translation image of the preimage, ABC. Answer: Yes, A''B''C'' is the translation image of ABC.

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