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?

a. 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.
b. Circle 1 and Circle 2 have the same area, and Circle 1 has a radius 0.625 times longer than Circle 2.
c. 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.
d. 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.

Answer 1

The correct answer is C.
Circle 1 has radius 8x. Circle 2 has radius 5x.
8x/5x = 1.6
Circle 1 is a dilation of Circle 2 with a scale factor of 1.6.
The radius of Circle 1 is 1.6 times greater than the radius of Circle 2.