Step-by-step explanation:
The rule that best represents the dilation applied to Circle | to create Circle || is the scale factor. The scale factor determines the ratio of corresponding lengths between the original figure (Circle |) and the dilated figure (Circle ||).
In a dilation, all lengths in the original figure are multiplied by the scale factor to obtain the corresponding lengths in the dilated figure. This includes the radii of the circles.
For example, if the scale factor is 2, it means that every length in the original figure is doubled in the dilated figure. If the scale factor is 1/2, it means that every length is halved. The scale factor can be greater than 1, less than 1 (but greater than 0), or even negative, indicating a reflection.
In the context of the given scenario, since the origin is the center of dilation, the scale factor determines how the distances from the origin to any point on Circle | are scaled to obtain the corresponding distances on Circle ||.
