Lesson 9-2 Translations

5-Minute Check on Lesson 9-1 Transparency 9-2 5-Minute Check on Lesson 9-1 Name the reflected image of each figure in line m BC AB ∆AGB B ABCF 6. How many lines of symmetry are in an equilateral triangle? DC ED ∆EGD D EDCF Standardized Test Practice: A 1 B 2 C C 3 D 4 Click the mouse button or press the Space Bar to display the answers.

Objectives Draw translated images using coordinates Draw translated images by using repeated reflections

Vocabulary Translation – transformation that moves all points of a figure the same distance in the same direction Composition – transformation made up of successive transformations (even number)

Translation Translation – a transformation that moves all points of a figure, the same distance and direction A(6,8) moved down 11 and left 9 to A’(-3, -3) B(8,5) moved down 11 and left 9 to B’(-1, -6) C(3,4) moved down 11 and left 9 to C’(-6, -7) y x y x A A(t=4) B C A(t=3) A(t=2) A’ A(t=1) B’ C’ A(t=0) Composition – transformation made up of successive transformations (animation); also could be successive reflections across parallel lines

COORDINATE GEOMETRY Parallelogram 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'. Example 2-1a

COORDINATE GEOMETRY Parallelogram LMNP has vertices L(–1, 2), M(1, 4), N(3, 2), and P(1, 0). Graph LMNP and its image for the translation (x, y)  (x + 3, y – 4). Answer: Example 2-1b

ANIMATION The 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. Example 2-2a

Subtract 1 from each side. 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. 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. (x, y) (–1, –1) (–1, –4) Add 1 to each side. Add 1 to each side. The translation is from raindrop 3 to raindrop 4. Answer: Example 2-2a

Answer: (x – 3, y – 1); (x + 2, y + 2) 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) Example 2-2b

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

Answer: Yes, A''B''C'' is the translation image of ABC. 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. Example 2-3b

Summary & Homework Summary: Homework: A translation moves all points of a figure the same distance in the same direction A translation can be represented as a composition of reflections Homework: pg 472-474; 8-10, 12-13, 17-19, 27