Question

dilation ( d_{v,\frac{2}{3}} ) was performed on a rectangle. how does the image relate to the pre - image? select three options.
the image is a reduction because ( 0lt nlt1 ).
the side lengths of the image are two - fifths the size of the corresponding side lengths of the pre - image.
the angles of the image are two - fifths the size of the angles of the pre - image.
the center of dilation is at point q.
the base of the image is two - fifths the size of the base of the pre - image.

Explanation:

Step1: Analyze dilation property

For a dilation \(D_{k}\), if \(0 < k<1\), it is a reduction. Here \(k = \frac{2}{5}\), so \(0<\frac{2}{5}<1\), the image is a reduction.

Step2: Analyze side - length relationship

In dilation \(D_{k}\), the side lengths of the image are \(k\) times the side lengths of the pre - image. Since \(k=\frac{2}{5}\), the side lengths (including the base) of the image are \(\frac{2}{5}\) of the corresponding side lengths of the pre - image.

Step3: Analyze angle relationship

In dilation, the angles of the image and the pre - image are congruent. So the statement about angles being \(\frac{2}{5}\) is wrong. Also, there is no information about the center of dilation being point \(Q\) from the general dilation formula \(D_{k}\) (the center is not specified in \(D_{k}\) notation unless otherwise stated in the problem context which is not here)

Answer:

The image is a reduction because \(0 < n<1\).
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.