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 the center of one circle rests on the edge of the other circle, 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.

Explanation:

Step1: Recall the definition of similar circles

Similar circles can be obtained by translation and dilation.

Step2: Calculate the scale factor

The scale factor \(k=\frac{\text{radius of circle }X}{\text{radius of circle }Y}\). Given radius of circle \(X = 6\) and radius of circle \(Y=2\), then \(k=\frac{6}{2}=3\).

Step3: Analyze the translation

To prove similarity, we first translate the circles so they share a common center point (translation does not change the shape and size, just the position). Then we dilate the smaller circle (circle \(Y\)) by the scale factor.

Answer:

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