Question

circle h is a dilation of circle g with point r as the center of dilation. what is the scale factor from circle g to circle h?
points a, b, c, and d are on circle g. how far are each of these points from the center of dilation, point r?

Explanation:

Step1: Determine the distance from each point to R

Assume each ring represents a unit distance.

• For point \(A\): The distance from \(R\) is \(2\) units.
• For point \(B\): The distance from \(R\) is \(2\) units.
• For point \(C\): The distance from \(R\) is \(2\) units.
• For point \(D\): The distance from \(R\) is \(2\) units.

Step2: Find the scale factor

Let's assume the radius of circle \(g\) (distance from \(R\) to points \(A,B,C,D\)) is \(r = 2\) and the radius of circle \(h\) is \(R= 6\) (by counting the rings).
The scale factor \(k=\frac{\text{radius of }h}{\text{radius of }g}\)
\(k = \frac{6}{2}=3\)

Answer:

• Distance from \(R\) for \(A\): \(2\)
• Distance from \(R\) for \(B\): \(2\)
• Distance from \(R\) for \(C\): \(2\)
• Distance from \(R\) for \(D\): \(2\)
• Scale factor: \(3\)