Question

Circle A has center of (2, 3), and a radius of 5 and circle B has a center of (1, 4), and a radius of 10. What steps will help show that circle A is similar to circle B? (6 points) Group of answer choices

Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.

Answer 1

The answer is: “Dilate circle A by a scale factor of 2.”

When figures are similar, they are proportional, meaning their angles remain congruent, but their side lengths increase or decrease predictably by a factor. For two figures to be similar, they must be the same shape. All circles are similar because they measure 360° and because circles are unique, so there are no “types” of circles.

Dilating a figure by a scale factor will show the figures are similar because circle A can exactly be formed into circle B by a scale factor of 2. Also note that circle A has a radius of 5, and circle B has a radius of 10. Therefore, doubling the radius of circle A would equal the radius of circle B, and because the radius is being doubled, every other measurement of the circle (like diameter and circumference) would be altered as well.