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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?
A) Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 4.
B) 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.
C) Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
D) 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.

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 A Translate the circles so they sh class=


Answer :

semsee45

Answer:

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

Step-by-step explanation:

To prove that two circles are similar:

  1. Center the smaller circle on the larger circle so that the two circles share a common center point.
  2. Identify the scale factor of dilation needed to increase the smaller circle to the size of the larger circle by dividing the radius of the larger circle by that of the smaller circle.

From inspection of the given diagram:

  • Radius of Circle X = 6 units
  • Radius of Circle Y = 2 units

Therefore, the scale factor of dilation is:

[tex]\implies \sf Scale \; factor =\dfrac{6}{2}=3[/tex]

Therefore, the steps that prove circles X and Y are similar:

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

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