Question

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.

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"

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