Questions: Dilation Dv · 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 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

Transcript text: Dilation $D_{\mathrm{v} \cdot \frac{2}{3}}$ was performed on a rectangle. How does the image relate to the pre-image? Select three options. The image is a reduction because $0

Solution

Solution Steps

Step 1: Analyze the dilation factor

The dilation factor is $\frac{2}{5}$, which is between 0 and 1. This indicates a reduction.

Step 2: Determine the effect on side lengths

Since the dilation factor is $\frac{2}{5}$, the side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image.

Step 3: Determine the effect on angles

Dilations preserve angle measures. Therefore, the angles of the image are the same size as the angles of the pre-image, not two-fifths the size.

Final Answer: The correct options are:

• 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.

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