The problem asks to describe the transformations needed to move a solid circle with center (2, 3) and radius 1 onto a dashed circle with center (6, 5) and radius 4. The transformations involve translation and dilation.

1. Problem Description

The problem asks to describe the transformations needed to move a solid circle with center (2, 3) and radius 1 onto a dashed circle with center (6, 5) and radius

4. The transformations involve translation and dilation.

2. Solution Steps

First, we need to translate the solid circle so that its center coincides with the center of the dashed circle. The solid circle's center is (2, 3) and the dashed circle's center is (6, 5).

To translate (2, 3) to (6, 5), we need to move it $6 - 2 = 4$ units horizontally (right) and $5 - 3 = 2$ units vertically (up). Therefore, we translate the solid circle 4 units to the right and 2 units up.

Next, we need to dilate the solid circle so that its radius matches the radius of the dashed circle. The solid circle has a radius of 1 and the dashed circle has a radius of

4. To dilate the solid circle from radius 1 to radius 4, we need to multiply the radius by a scale factor of $4/1 = 4$. Therefore, the scale factor is

4.

3. Final Answer

Translate the solid circle right by 4 unit(s) and up by 2 unit(s).

Dilate the solid circle by a scale factor of 4.