Question

Suppose x is any positive number.

Circle 1: center (−7, 4) and radius 8x
Circle 2: center (−7, 4) and radius 2x
Why is circle 1 similar to circle 2?

A: Circle 1 and circle 2 have the same diameter.
B: Circle 1 is a dilation of circle 2 with a scale factor of 4.
C: Circle 1 is congruent to circle 2.
D: Circle 1 is a dilation of circle 2 with a scale factor of 0.25.

Answer 1

B: Circle 1 is a dilation of circle 2 with a scale factor of 4.

Answer 2

Option B: Circle
`1` is a dilation of circle
`2` with a scale factor of
`4`

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

All circles are similar and the scale factor is equal to the ratio of its radius or the ratio of its diameters or the ratio of its circumferences

Let

z------> the scale factor

A----> the radius of circle 1

B-----> the radius of circle 2

so

`z=(A)/(B)`

we have

`A=8x\ units`

`B=2x\ units`

`z=(8x)/(2x)=4`

The dilation is an enlargement because the scale factor is greater than
`1`