Question

dilation ( d_{v,\frac{2}{5}} ) was performed on a rectangle. how does the image relate to the pre - image? choose three correct answers.
the center of dilation is at point ( q ).
the side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image.
the base of the image is two - fifths the size of the base of the pre - image.
the image is a reduction because ( 0 < n < 1 ).
the angles of the image are two - fifths the size of the angles of the pre - image.

Explanation:

Step1: Recall Dilation Properties

Dilation scales lengths (sides, bases) by the scale factor \( n=\frac{2}{5} \), which is between 0 and 1, so it's a reduction. Angles remain equal (not scaled) in dilation.

Step2: Analyze Each Statement

• "The side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image": True, since dilation scales side lengths by \( \frac{2}{5} \).
• "The base of the image is two - fifths the size of the base of the pre - image": True, as base length is a side length, scaled by \( \frac{2}{5} \).
• "The image is a reduction because \( 0 < n<1 \)": True, since \( \frac{2}{5}=0.4 \) and \( 0 < 0.4<1 \), so it's a reduction.
• "The center of dilation is at point Q": The problem is about how the image relates to the pre - image (scaling, reduction, side/base lengths), not the center's location, so this is irrelevant.
• "The angles of the image are two - fifths the size of the angles of the pre - image": False, angles are congruent in dilation.

Answer:

1. The side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image.
2. The base of the image is two - fifths the size of the base of the pre - image.
3. The image is a reduction because \( 0 < n<1 \).