Identify the transformation that carries the figure onto itself.
a) reflect across the line y = 7 and rotate 270° clockwise about (−7, 8)
b) reflect across the line x = 7 and rotate 270° clockwise about (−7, 8)
c) reflect across the line y = −7 and rotate 540° clockwise about (−7, 8)
d) reflect across the line x = −7 and rotate 540° clockwise about (−7, 8)

The correct option is D.

Step-by-step explanation:

The vertices of given figure are (-9,8), (-7,7), (-5,8), (-7,9).

1. If figure reflect across the line y = 7, then

The vertices of image are (-9,6), (-7,7), (-5,6), (-7,5).

Then rotate 270° clockwise about (−7, 8).

The vertices of image are (-5,6), (-6,8), (-5,10), (-4,8). These are not the vertices of given figure, theretofore option A is incorrect.

2. If figure reflect across the line x = 7, then

The vertices of image are (23,8), (21,7), (19,8), (21,9).

Then rotate 270° clockwise about (−7, 8).

The vertices of image are (-7,38), (-6,36), (-7,34), (-8,36). These are not the vertices of given figure, theretofore option B is incorrect.

3. If figure reflect across the line y = -7, then

The vertices of image are (-9,-22), (-7,-21), (-5,-22), (-7,-23).

Then rotate 540° clockwise about (−7, 8).

The vertices of image are (-5,38), (-7,37), (-9, 38), (-7.39). These are not the vertices of given figure, theretofore option C is incorrect.

4. If figure reflect across the line x = -7, then

The vertices of image are (-5,8), (-7,7), (-9,8), (-7,9).

Then rotate 540° clockwise about (−7, 8).

The vertices of image are (-9,8), (-7,9), (-5,8), (-7,7). These are the vertices of given figure, theretofore option D is correct.

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step-by-step explanation: