Circle f is a dilation of circle e with point R as the center of dilation.
What is the scale factor that takes the smaller circle, circle e, to the larger circle, circle f?
Distance from R	
Point on
circle e	Corresponding
point on
circle f	Scale Factor
A	2	8	
B	2	8	
C	2	8	
D	2	8	


The scale factor of a dilation is the ratio of the distance from the center of dilation to a point on the image to the distance from the center of dilation to the corresponding point on the preimage. 

In this case, the distance from point R (the center of dilation) to each point on circle e is 2, and the distance from R to the corresponding points on circle f is 8. The scale factor \( k \) is calculated as:

\[
k = \frac{\text{distance from R to point on circle f}}{\text{distance from R to point on circle e}} = \frac{8}{2} = 4
\]

Thus, the scale factor is 4.

Would you like further details on how dilation works or have any additional questions?

Here are 5 related questions to explore further:
1. What is the general effect of a dilation on the size of a geometric shape?
2. How do you find the center of dilation given two corresponding points?
3. What happens if the scale factor is less than 1 in a dilation?
4. How does the area of a shape change when it is dilated by a certain scale factor?
5. What are other transformations besides dilation that can alter the size of a figure?

**Tip:** The scale factor also applies to the ratio of corresponding lengths (such as radius) between the original and the dilated shape.

Circle f is a dilation of circle e with point R as the center of dilation. What is the scale factor that takes the smaller circle, circle e, to the larger circle, circle f? Distance from R: Point on circle e: 2, Corresponding point on circle f: 8

Explore how to find the scale factor in a dilation problem where circle e is dilated to circle f with point R as the center. Learn the step-by-step method to calculate the scale factor based on the distances from the center of dilation. Suitable for students in Grades 8-10.

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