To transform Pentagon ABCDE into Pentagon VWXYZ while maintaining their similarity, we need to consider the scale factor between their perimeters.
The perimeter of ABCDE is 36 m and the perimeter of VWXYZ is 18 m. To find the scale factor, we can divide the perimeter of ABCDE by the perimeter of VWXYZ:
\[ \text{Scale Factor} = \frac{\text{Perimeter of ABCDE}}{\text{Perimeter of VWXYZ}} = \frac{36}{18} = 2 \]
Since VWXYZ is smaller than ABCDE, the appropriate scale factor for the transformation will be \(\frac{1}{2}\) (indicating that VWXYZ is half the size of ABCDE, not bigger).
Now let's analyze the given options for transformations:
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A dilation with a scale factor of 2 followed by a rotation of 90 degrees clockwise: This will not produce Pentagon VWXYZ because the dilation is incorrect (it enlarges rather than shrinks).
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A translation to the right followed by a dilation with a scale factor of 1/2: While the dilation is correct (it will reduce the size of the pentagon), the translation may not be necessary depending on the position of the pentagons.
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A reflection over a vertical line followed by a dilation with a scale factor of 1/2: This is a valid sequence since the reflection can reposition the pentagon, and the dilation will properly shrink it down to the appropriate size.
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A rotation of 180 degrees counterclockwise followed by a dilation with a scale factor of 2: Similar to the first option, the dilation is incorrect (it enlarges rather than reduces).
Based on the understanding from the options provided, the best choice is:
A reflection over a vertical line followed by a dilation with a scale factor of 1/2.