The problem asks us to describe the transformations necessary to move a solid circle with center (5, 7) and radius 2 exactly onto a dashed circle with center (3, 5) and radius 1. We need to determine the translation needed and the scale factor for dilation. We also need to determine if the two circles are similar.

1. Problem Description

The problem asks us to describe the transformations necessary to move a solid circle with center (5, 7) and radius 2 exactly onto a dashed circle with center (3, 5) and radius

1. We need to determine the translation needed and the scale factor for dilation. We also need to determine if the two circles are similar.

2. Solution Steps

First, we need to find the translation vector to move the center of the solid circle to the center of the dashed circle. The center of the solid circle is (5, 7) and the center of the dashed circle is (3, 5). To move the solid circle's center to the dashed circle's center, we need to subtract the coordinates of the solid circle's center from the dashed circle's center. This gives us (3 - 5, 5 - 7) = (-2, -2). Thus, we translate the solid circle by 2 units to the left and 2 units down. "Left" corresponds to a negative change in the x-coordinate and "down" corresponds to a negative change in the y-coordinate.

Next, we need to find the scale factor for the dilation. The radius of the solid circle is 2 and the radius of the dashed circle is

1. To transform the solid circle to have the same size as the dashed circle, we need to dilate it by a scale factor of $\frac{1}{2}$.

Finally, all circles are similar to each other, regardless of their radii.

3. Final Answer

Translate the solid circle by 2 unit(s) to the left and 2 unit(s) down.

Dilate the solid circle by a scale factor of $\frac{1}{2}$.

The original solid circle and the dashed circle are similar: Yes.