Question

Which transformation shows that the two given circles are similar?

Circle A -- center(2, 0), radius 8
Circle A' -- center(-1, 5), radius 3

A)(x, y) → (x - 3, y + 5); scale factor 3/8
B)(x, y) → (x - 3, y + 5); scale factor 8/3
C)(x, y) → (x + 3, y - 5); scale factor 3/8
D)(x, y) → (x + 3, y - 5); scale factor 8/3

Answer 1

What we know:
Circle A has a center at (2,0) and a radius of 8
Circle A' has a center at (-1,5) and a radius of 3

What we need to find:
we need to find the transformation from the center point of A to A' and the scale factor

Circle A can be mapped to Circle A'
center point translation (x,y)⇒[(x+a),(y+b)]⇒(x-3, y+5)

2+a=-1 0+b=5
-2+2+a=-1-2 b=5
a=-3

scale factor is 3/8
8x=3
8/8x=3/8
x=3/8

A)(x, y) → (x - 3, y + 5); scale factor 3/8