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Chapter 9.2

Translations. Translations. Translations. Translations. Translations. Translations. Translations. Translations. Chapter 9.2. Translations. Translations. Translations. Translations. Translations. Draw translated images using coordinates. translation. composition.

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Chapter 9.2

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  1. Translations Translations Translations Translations Translations Translations Translations Translations Chapter 9.2 Translations Translations Translations Translations Translations

  2. Draw translated images using coordinates. • translation • composition • Draw translated images by using repeated reflections. Standard 22.0 Students know the effect of rigid motions on figures in the coordinate planeand space, including rotations, translations,and reflections. (Key) Lesson 2 MI/Vocab

  3. Translation • A transformation that maps every two points P and Q to points P’ and Q’, so that the following properties are true: • PP’ = QQ’ • PP’ // QQ’, or PP’ and QQ’ are collinear • Is a composite of two reflections over // lines

  4. Translations in the Coordinate Plane Triangle TUV has vertices T(–1, –4), U(6, 2), and V(5, –5). If ΔTUV is translated 3 units up and 5 units left to create ΔT'U'V', what are the coordinates of the vertices of ΔT'U'V'? Lesson 2 Ex1

  5. U V T U’ T’ V’ Plot points T(–1, –4), U(6, 2), and V(5, –5). Do not translate the triangle!!! Translate the vertices 3 units up and 5 units left. Then connect the dots to create ΔT'U'V', T’: (-6, -1) U’: (1, 5) V’: (0, -2)

  6. Translations in the Coordinate Plane Solve the Item (quicker with math!) “Three units up”  y + 3 “Five units left”  x – 5 (x, y)  (x – 5, y + 3). T(–1, –4) T' (–1 – 5, –4 + 3) or T' (–6, –1) U(6, 2) U' (6 – 5, 2 + 3) or U' (1, 5) V(5, –5) V' (5 – 5, –5 + 3) or V' (0, –2) Lesson 2 Ex1

  7. Translations in the Coordinate Plane Triangle ABC has vertices A(-2, 3), B(4, -1), and C(-5, -3). If ΔABC is translated 4 units down and 3 units right to create ΔA'B'C', what are the coordinates of the vertices of ΔA'B'C'? A'(1, -1), B'(7, -5), C'(-1, -7) Lesson 2 Ex1

  8. A.B. C.D. 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). • A • B • C • D Lesson 2 CYP1

  9. Repeated Translations ANIMATION The graph shows repeated translations that result in the animation of a raindrop. Find the translation that moves raindrop 2 to raindrop 3. x – 2 y – 3 The translation from raindrop 2 to raindrop 3 is (x – 2, y – 3) Lesson 2 Ex2

  10. Repeated Translations ANIMATION The graph shows repeated translations that result in the animation of a raindrop. Find the translation that moves raindrop 3 to raindrop 4. x + 0 y - 3 The translation from raindrop 3 to raindrop 4 is (x, y – 3) Lesson 2 Ex2

  11. A. 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. • A • B • C • D A.(x + 3, y + 1) B.(x – 3, y – 1) C.(x + 3, y – 1) D.(x – 3, y + 1) Lesson 2 CYP2

  12. B. ANIMATION The graph shows repeated translations that result in the animation of a lightning bolt. Find the translation that moves lightning bolt 2 to lightning bolt 1. • A • B • C • D A. (x + 2, y + 2) B. (x – 2, y – 2) C. (x + 2, y – 2) D. (x – 2, y + 2) Lesson 2 CYP2

  13. Find a Translation Using Reflections In the figure, lines p and q are parallel. Determine whether the red figure is a translation image of the blue preimage, quadrilateral EFGH. Answer: Quadrilateral E''F''G''H'' is not a translation image of quadrilateral EFGH. Lesson 2 Ex3

  14. In the figure, lines n and m are parallel. Determine whether ΔA''B''C'' is a translation image of the preimage, ΔABC. • A • B • C A. yes B. no C. cannot be determined Lesson 2 CYP3

  15. Homework Chapter 9-2 Pg 506 2 – 10 even, 12 – 17 all, 24, 26, and 39

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