Question

two circles have radii r1 = 7 and r2 = 21. what is the scale factor (k) for the dilation?
a. 4.25
b. 3
c. 25
d. 2

if two circles have radii r1 = 4 and r2 = 12, what is the scale factor needed to map the smaller circle onto the larger circle?
a. 25
b. 3
c. 2
d. 15

a smaller circle with a radius of 2 and center (-5,4) needs to be transformed into a larger circle with a radius of 10 and center (3, -2). what transformations are needed?
a. dilation and translation
b. dilation only
c. reflection and dilation
d. translation only

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ for a dilation of circles is given by $k=\frac{r_2}{r_1}$, where $r_2$ is the radius of the dilated circle and $r_1$ is the radius of the original circle.

Step2: Calculate scale factor for first pair

Given $r_1 = 7$ and $r_2=21$, then $k=\frac{21}{7}=3$.

Step3: Calculate scale factor for second pair

Given $r_1 = 4$ and $r_2 = 12$, then $k=\frac{12}{4}=3$.

Step4: Analyze circle transformation

The radius changes from 2 to 10, so a dilation with scale - factor $k=\frac{10}{2}=5$ is needed. The center changes from $(-5,4)$ to $(3, - 2)$, so a translation is also needed.

Answer:

1. B. 3
2. B. 3
3. A. Dilation and translation