Question

Suppose x is any positive number why is circle 1 similar to circle

circle 1: center (0,0) and radius 2x
circle 2: center (0,0) and radius 10x

A circle 2 is a dilation of circle 1 with a scale factor of 5

B circle 2 is a dilation of circle 1 with a scale factor of 8

C circle and circle 2 have equal areas

D both circles are centered at the origin

Answer 1

A circle 2 is a dilation of circle 1 with a scale factor of 5

Explanation:

We have been given information about two circles as given below:

circle 1: center (0,0) and radius 2x

circle 2: center (0,0) and radius 10x .

Now we need to find about why is circle 1 similar to circle where x is any positive number.

We know that all circles are similar. So after dilation it doesn't affect their similarities.

10x can be obtained from 2x, by multiplying 2x with 5.

So the first choice "A circle 2 is a dilation of circle 1 with a scale factor of 5" is correct.