Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.

From A to B: (x - 2, y + 1), scale factor 2?

Yes, but a proof explaining the translation and scale factor is expected in my quiz. So would the answer be correct in this case?

translation is correct

scale factor of radii is 2
scale factor of area is 4 , you didn't say what scale factor

To prove that two circles are similar, we need to show that their corresponding parts (center and radius) have a constant ratio.

Let's start by finding the distance between the centers of the two circles:

Distance between the centers:
To find the distance between two points, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)

For circle A with center (-1, 1):
x1 = -1, y1 = 1

For circle B with center (-3, 2):
x2 = -3, y2 = 2

Using the distance formula, we can calculate the distance between the centers:
d = √((-3 - (-1))^2 + (2 - 1)^2)
= √((-3 + 1)^2 + 1^2)
= √((-2)^2 + 1)
= √(4 + 1)
= √5

Now let's compare the radii of the two circles:

Radius of circle A: r1 = 1
Radius of circle B: r2 = 2

To check if the circles are similar, we need to make sure the ratio of the radii is equal to the ratio of the distances between the centers:

Ratio of radii:
r2/r1 = 2/1 = 2

Ratio of distances between the centers:
d/d1 = √5/1

Since the ratio of r2/r1 is equal to the ratio of d/d1 (√5/1), we can conclude that circle A and circle B are similar.

Regarding the transformation you mentioned, from A to B: (x - 2, y + 1), this doesn't represent a scale factor of 2. It appears to be a translation, where each x-coordinate is shifted 2 units to the left and each y-coordinate is shifted 1 unit up.

Your question makes no sense to me.

All circles are "similar" to each other.