Circle a has center of (4, 6) and a radius of 5, and circle b has a center of (1, 0) and a radius of 15. what steps will show that circle a is similar to circle b?

dilate circle a by a scale factor of 3.
translate circle a using the rule (x − 3, y + 6).
rotate circle a 180° about the center.
reflect circle a over the y-axis.

Explanation:

To show that the circle A is similar to circle B you can use any set of transformations that preserve the angles: translations, reflections, rotations, dilations, and combinations of them are the transformations that meet the required conditions.

By translating the circle A such that the center of its image concide with the the center of the circle B, and then dilating it by a scale factor that dilates the radius to the same size of the radius of B, you will have shown that both circles are similar.

First, lets think about the translation. The center of the circle A (4,6) must be translated to the point (1,0), which is the center of the circle B.

That means that the coordinate 4 must be shifted 3 units to the left (x → x - 3), and the coordinate 6 must be shifted 6 units downward (y → y - 6). Then, the rule for the translation is (x - 3, y - 6).

Now, lets consider the dilation. The radius of circle A is 5 and tis image shall have a radius of 15, which is the radius of the circle B. That means that the dilation's scale factor is 15:5 = 3. So, dilate the circle A by a scale factor of 3.

Finally, the answer is:

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step-by-step explanation: