Question

dilation $d_{q,\frac{2}{5}}$ was performed on a rectangle. how does the image relate to the pre - image? select three options.

• the image is a reduction because $0 < n < 1$.
• 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:

Dilation \(D_{Q,\frac{2}{5}}\) has center \(Q\) and scale factor \(\frac{2}{5}\). A scale factor between 0 and 1 means reduction. Side lengths (including base) scale by \(\frac{2}{5}\), but angles remain equal in dilation.

Answer:

A. The image is a reduction because \(0 < n < 1\), B. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image, D. The center of dilation is at point Q, E. The base of the image is two-fifths the size of the base of the pre-image.

Wait, correction: The question says select three options. Let's recheck:

1. Reduction (0<2/5<1): correct.
2. Side lengths scale by 2/5: correct.
3. Angles stay same: incorrect.
4. Center is Q: correct (from notation \(D_{Q,\frac{2}{5}}\)).
5. Base (a side length) scales by 2/5: correct.

But if only three, likely the first, second, and fifth (or first, second, fourth). Assuming standard selection: