Which sequence of transformations will map figure H onto figure H′?Two congruent hexagons are shown on a coordinate plane; hexagon H quadrant one with vertices at 2 comma 2, 2 comma 6, 6 comma 7, 8 comma 6, 8 comma 2, and 6 comma 1; hexagon H prime with vertices at 2 comma negative 8, 2 comma negative 4, 4 comma negative 3, 8 comma negative 4, 8 comma negative 8, and 4 comma negative 9. Rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across x = −6 Rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6 Rotation of 180° about the origin, translation of (x − 10, y + 2), and reflection across y = −6 Rotation of 180° about the origin, translation of (x − 10, y + 2), and reflection across x = −6

Answer:

Rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6

Step-by-step explanation:

The sequence of transformations that will map figure H onto figure H' is the rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6.

Given :

Points of Hexagon H  --  (2,2), (2,6), (6,7), (8,6), (8,2), (6,1)

Points of Hexagon H' --  (2,-8), (2,-4), (4,-3), (8,-4), (8,-8), (4,-9)

The following steps can be used to transform the hexagon H into hexagon H':

Step 1 - Translate the hexagon in the positive x-axis direction by a factor of 10.

Step 2 - Translate the graph obtained in the above step by factor 2 in the downward direction.

Step 3 - Now, rotate the graph obtained in the above step 180 degrees about the origin.

Step 4 - Then take the reflection of the graph obtained in the above step about y = -6. The resulting graph shows the graph of Hexagon H'.

Therefore, the correct option is B).

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