The problem involves finding the scale factor and center of dilation for a transformation between two circles on a coordinate plane.

Observations from the image:

1. Circles: There are two circles, $F$ and $F'$. The smaller circle $F$ is dilated to form the larger circle $F'$.
2. Centers and Radii:
   • The center of circle $F$ is at $(0, 0)$, and its radius (from $F$ to $G$) is measured as 2 units.
   • The center of circle $F'$ is also at $(0, 0)$, and its radius (from $F'$ to $G'$) is measured as 10 units.

Step-by-step solution:

1. Scale Factor:

The scale factor $k$ for dilation is given by the ratio of the radius of the dilated circle ($F'$) to the original circle ($F$): $k = \frac{\text{Radius of } F'}{\text{Radius of } F} = \frac{10}{2} = 5.$

2. Center of Dilation:

Both circles $F$ and $F'$ have the same center at $(0, 0)$, so the center of dilation is: $(0, 0).$

Final Answer:

• Scale Factor: $5$
• Center of Dilation: $(0, 0)$

Would you like further details on this explanation?

Related Questions:

1. How do you determine the radius of a circle on a coordinate plane from its graph?
2. What happens to the area of a circle after dilation with a scale factor $k$?
3. How do you verify the center of dilation using coordinates?
4. If a circle is dilated with a scale factor less