chapter 9.2
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Translations. Translations. Translations. Translations. Translations. Translations. Translations. Translations. Chapter 9.2. Translations. Translations. Translations. Translations. Translations. Draw translated images using coordinates. translation. composition. - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 9.2
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• 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)
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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
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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
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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)
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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
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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)
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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.
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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)
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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
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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)
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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)
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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.
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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.
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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