In a dilation, the image and the pre-image have a specific relationship based on the scale factor. Here are the correct statements related to the dilation \( D_V \left( \frac{2}{5} \right) \) performed on a rectangle:
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The image is a reduction because \( 0 < n < 1 \).
- This is true because a scale factor less than 1 (in this case, \( \frac{2}{5} \)) indicates a reduction.
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The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.
- This is also true as the side lengths of the image after the dilation would indeed be two-fifths the lengths of the corresponding sides in the pre-image.
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The base of the image is two-fifths the size of the base of the pre-image.
- This statement is true as well; specifically for the base of the rectangle, it will also be reduced to two-fifths of its original length.
The following options can be ruled out:
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The angles of the image are two-fifths the size of the angles of the pre-image.
- This is false because dilation does not change the angles of the shape; the angles remain the same in both the pre-image and the image.
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The center of dilation is at point Q.
- This statement cannot be evaluated without additional context about the location of point Q, so we cannot confirm this without more information.
Therefore, the three correct statements are the first, second, and third options.