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

Solution:

Given, a regular hexagon with a center (-7, 3.5)

We have to identify the transformation that maps the given regular hexagon onto itself.

A regular hexagon has 6 axes of symmetry.

So, the angle of rotational symmetry is given by 360 divided by the number of sides.

Angle of rotational symmetry = 360/6 = 60 degrees

Since 90 degrees is not a multiple of 60 degrees, options A and B cannot be true.

120 degrees is a multiple of 60 degrees.

So, the regular hexagon is rotated clockwise at 120º.

When we reflect a point across the line y=x, the x-coordinate, and y-coordinate change places.

From the point (-7, 3.5)

x = -7

This implies that the reflection across the line is x = -7.

Therefore, the hexagon rotates 120° clockwise about (-7, 3.5) and reflects across the line x = -7.

Identify the transformation that maps the regular hexagon with a center (-7, 3.5) onto itself

Summary:

The transformation that maps the regular hexagon with a center (-7, 3.5) onto itself is that the hexagon rotates 120° clockwise about (-7, 3.5) and reflects across the line x = -7.