Translations Translations Chapter 9.2 Translations Translations Translations Translations Translations Translations Translations Translations Translations Translations Translations

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 plane and space, including rotations, translations, and reflections. (Key) Lesson 2 MI/Vocab

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

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

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’ U’: (1, 5) U V’: (0, -2) V’ T’ T V

Solve the Item (quicker with math!) 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

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

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. A B C D Lesson 2 CYP1

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

The translation from raindrop 3 to raindrop 4 is (x, y – 3) 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

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

A. (x + 2, y + 2) B. (x – 2, y – 2) C. (x + 2, y – 2) 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. (x + 2, y + 2) B. (x – 2, y – 2) C. (x + 2, y – 2) D. (x – 2, y + 2) A B C D Lesson 2 CYP2

In the figure, lines p and q are parallel. 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

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

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