Question

Circle A has a center of (4, 5), and a radius of 3, and circle B has a center of (1, 7), and a radius of 9. What steps will help show that circle A is similar to circle B? (6 points)

a) Translate circle A using the rule (x+3,y−2).

b) Dilate circle A by a scale factor of 3.

c) Rotate circle A 90° about the center.

d) Reflect circle A over the x-axis.

Answer 1

To show circle A is similar to circle B, the best option is to dilate circle A by a scale factor of 3, which resizes it without changing its shape to match the size of circle B.

Step-by-step explanation:

To determine whether circle A is similar to circle B, we need to consider the properties of similarity for circles. Circles are similar if they have the same shape but may differ in size. Thus, we look for transformations that change size but not shape. Step b) Dilate circle A by a scale factor of 3, seems most appropriate. This is because the radius of circle B is 9, which is three times the radius of circle A, which is 3. By dilating circle A by a scale factor of 3, we change its size to match circle B without altering its shape.

• Translating circle A would not change the size of the circle, so option a) is not correct.
• Scaling circle A by a factor of 3 would create a circle similar to circle B, making option b) correct.
• Rotating circle A would not change its size or position relative to circle B, so option c) is not correct.
• Reflecting circle A over the x-axis would not change the size, so option d) is not correct.