Question

circle x with a radius of 6 units and circle y with a radius of 2 units are shown. which steps would prove the circles similar? translate the circles so they share a common center point, and dilate circle y by a scale factor of 4. translate the circles so they share a common center point, and dilate circle y by a scale factor of 3. translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle y by a scale factor of 3. translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle y by a scale factor of 4.

Explanation:

Step1: Recall similarity of circles

Two circles are similar if one can be obtained from the other by translation and dilation. The ratio of the radii of two similar circles is the scale - factor of dilation.

Step2: Calculate the scale - factor

The radius of circle X is \(r_X = 6\) units and the radius of circle Y is \(r_Y=2\) units. The scale - factor \(k\) of dilating circle Y to make it congruent to circle X is \(k=\frac{r_X}{r_Y}=\frac{6}{2} = 3\). First, we need to translate the circles so they share a common center point (translation does not change the shape or size, just the position). Then we dilate circle Y by a scale factor of 3.

Answer:

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.