Question

in the graph below, circle p is the image of circle p after a dilation. radii (overline{pq}) and (overline{pq}) are also shown. what are the scale factor and center of the dilation? simplify your answers and write them as fractions or whole numbers. scale factor: center of the dilation: (, )

Explanation:

$k=\frac{r_2}{r_1}=\frac{2}{6}=\frac{1}{3}$.

Step3: Determine center of dilation

The center of dilation is the fixed point. Since the position of point $P(3,2)$ and $P'(3,4)$ and other corresponding points are related in such a way that the point $(3,2)$ is the center of dilation (because the distance from the center to corresponding points changes according to the scale factor and the center does not move during dilation).

Answer:

scale factor: $\frac{1}{3}$
center of the dilation: $(3,2)$