Which sequence of transformations will map figure K onto figure K′? Two congruent kites, figure K and figure K prime, are drawn
on a coordinate grid. Figure K has vertices at 4, 3, at 6, 5, at 4, 8, and at 2, 5. Figure K prime has vertices at 4, negative 8, at 6, negative 5, at 4, negative 3, and at 2, negative 5 Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y) Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y) Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y) Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)
2 answers:
Answer:
The sequence of transformations will map figure K onto figure K′
is the first sequence <u>option (1)</u>
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Step-by-step explanation:
See the attached figure
as shown in the figure the K' is the image of K by reflection over x-axis
<u>But </u> We need to know which sequence of transformations will give the same result.
So, we will test the options by any point from K and its image from K'
i.e: we will test the options using the points (6,5) , (6,-5)
(6,5) ⇒ (6,-5)
<u>option (1):</u>
Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y)
(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (6,-5)
<u>option (2):</u>
Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y)
(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (-10,-5)
<u>option (3):</u>
Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)
(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (2,-3)
<u>option (4):</u>
Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)
(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (-14,-3)
As shown: The sequence of transformations will map figure K onto figure K′
is the first sequence <u>option (1)</u>
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