Suppose x is any positive number. Circle 1 has a center at (-2, 7) and a radius of 8x. Circle 2 has a center at (-3, 0) and a radius of 5x. Why is Circle 1 similar to Circle 2? Circle 1 and Circle 2 have the same area, and Circle 1 has a radius 0.625 times longer than Circle 2. Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6. Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 0.625. Circle 1 and Circle 2 have the same circumference, and Circle 1 has a radius 1.6 times the length of Circle 2's radius.

Question

Mathematics

Karissa Dougherty

16 June, 05:14

Suppose x is any positive number. Circle 1 has a center at (-2, 7) and a radius of 8x. Circle 2 has a center at (-3, 0) and a radius of 5x. Why is Circle 1 similar to Circle 2? Circle 1 and Circle 2 have the same area, and Circle 1 has a radius 0.625 times longer than Circle 2. Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6. Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 0.625. Circle 1 and Circle 2 have the same circumference, and Circle 1 has a radius 1.6 times the length of Circle 2's radius.

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Answers (1)

Know the Answer?

Christina Singleton · Answer 1

The correct answer is "Circle 1 is a translation of 1 unit right and 7 units up from Circle 2, and a dilation of Circle 2 with a scale factor of 1.6"

Step-by-step explanation:

We can tell this because first they identify the movement properly. When going from (-3, 0) to (-2, 7), we move to the right one and up 7.

Also, we know there is a scale factor of 1.6, because when we look at the radius of each circle, we can divide and find that factor.

8x/5x = 1.6