Chapter 9.2

• translation• composition

• Draw translated images using coordinates.

• 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)

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

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'?

Translations in the Coordinate Plane

T’

U’

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)

U

VT

V’: (0, -2)

Solve the Item (quicker with math!)

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)

Translations in the Coordinate Plane

(x, y) (x – 5, y + 3).

“Three units up” y + 3“Five units left” x – 5

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)

A. A

B. B

C. C

D. D0% 0%0%0%

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.

ANIMATION The graph shows repeated translations that result in the animation of a raindrop.

Find the translation that moves raindrop 2 to raindrop 3.

Repeated Translations

y – 3

x – 2

The translation from raindrop 2 to raindrop 3 is (x – 2, y – 3)

ANIMATION The graph shows repeated translations that result in the animation of a raindrop.

Find the translation that moves raindrop 3 to raindrop 4.

Repeated Translations

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

y - 3

x + 0

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

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)

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

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)

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.

1. A

2. B

3. C

0% 0%0%

A. yes

B. no

C. cannot be determined

In the figure, lines n and m are parallel. Determine whether ΔA''B''C'' is a translation image of the preimage, ΔABC.

HomeworkHomework

Chapter 9-2Chapter 9-2

Pg 506Pg 506

2 – 10 even, 12 – 17 all, 24, 26, and 392 – 10 even, 12 – 17 all, 24, 26, and 39