Question

dilation ( d_{v,\frac{2}{5}} ) 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 \(D_{v,k}\), 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

The scale factor \(k=\frac{2}{5}\). For a dilation, if the pre - image has side length \(l\), the image side length \(l'=k\times l\). So the side lengths of the image are \(\frac{2}{5}\) of the pre - image.

Step3: Analyze angle relationship

In a dilation, the angles of the pre - image and the image are congruent. So the statement "The angles of the image are two - fifths the size of the angles of the pre - image" is wrong.

Step4: Analyze center of dilation

The center of dilation is \(v\) (from the notation \(D_{v,\frac{2}{5}}\)), not \(Q\). So the statement "The center of dilation is at point \(Q\)" is wrong.

Step5: Analyze base (a type of side)

Since the scale factor \(k = \frac{2}{5}\), if the base of the pre - image is \(b\), the base of the image \(b'=\frac{2}{5}b\).

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.