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
5/11
11/5
5
11
translate one of the circles so that the circles have the same center.

Explanation:

Step1: Recall the property of similar circles

All circles are similar. For two circles with radii \(r_1\) and \(r_2\), a dilation (a transformation that changes the size of a figure) can be used to map one circle to another. If we have a smaller circle with radius \(r_1 = 5\) and a larger circle with radius \(r_2=11\), the scale factor \(k\) of the dilation that maps the smaller circle to the larger circle is given by the formula \(k=\frac{r_2}{r_1}\).

Step2: Calculate the scale factor

Substitute \(r_1 = 5\) and \(r_2 = 11\) into the formula \(k=\frac{r_2}{r_1}\). We get \(k=\frac{11}{5}\). When we dilate the smaller circle (with radius \(r = 5\)) by a factor of \(\frac{11}{5}\), the radius of the dilated circle is \(5\times\frac{11}{5}=11\), which is the radius of the larger circle.

Answer:

\(\frac{11}{5}\)