Question

performing transformations on circles
concentric circles with center g have radii 5 and 11 as shown.
which would prove that the circles are similar?
dilate the smaller circle by a factor of
if the circles were not concentric, what additional step would be
needed to prove they are similar?
one of the circles so that the circles have the same
center.

Explanation:

Step1: Find the dilation factor

To make the smaller circle (radius \(r_1 = 5\)) congruent to the larger circle (radius \(r_2=11\)) after dilation, we use the formula for dilation factor \(k=\frac{r_2}{r_1}\).

$$k=\frac{11}{5}= 2.2$$

Step2: Determine the transformation for non - concentric circles

If the circles are not concentric, we need to use a translation. A translation moves a figure without changing its shape or size. We would translate one of the circles so that their centers coincide.

Answer:

Dilate the smaller circle by a factor of \(2.2\). Translate one of the circles so that the circles have the same center.