Question

Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Circles X and Y are shown. Circle X has a radius of 6 units and circle Y has a radius of 2 units. 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.

Answer 1

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

Explanation:

To prove circles are similar:

• Translate the circles so that they share a common center point. (The circles are now concentric as they have the same center).
• Dilate the smaller circle to increase its size to coincide with the larger circle. The amount that the circle needs to be dilated by is the scale factor.

As the radius of circle Y is 2 and the radius of circle X is 6, determine the scale factor by dividing the larger radius by the smaller radius:

scale factor = 6 ÷ 2 = 3

Solution

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

Answer 2

The scale is 6/2 = 3

tanslate the circles to have the same center point and scale circle y by a factor of 3.

The answer is C.