Identify the transformation that maps the regular hexagon with a center (-7, 3.5) onto itself. a) rotate 90° clockwise about (-7, 3.5) and reflect across the line x = -7 b) rotate 90° clockwise about (-7, 3.5) and reflect across the line y = 3.5 c) rotate 120° clockwise about (-7, 3.5) and reflect across the line x = -5 d) rotate 120° clockwise about (-7, 3.5) and reflect across the line x = -7

The answer is D.

When you rotate a plane around its center with its angle of rotational symmetry, it will map onto itself.

In this example, we have a regular hexagon which has 6 axes of symmetry.

To find its angle of rotational symmetry, we need to divide 360 by its number of AoS.

In this example, 360 / 6 = 60 degrees is the angle of rotational symmetry.

Since 90 is not a multiple of 60, we will eliminate choices A and B.

In C it says "reflect across the line x = -5" which isn't an AoS of the hexagon.

Lastly, in D, we need to "rotate 120 (which is a multiple of 60)", and "reflect across x = -7 (which is an AoS of the regular hexagon)". And it maps onto itself.

The answer to your question is D

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