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

Answer 1

Translate Circle A (x-3, y+5) and then dilate by a scale factor of 3/8 or 0.375

Answer 2

Explanation:

One circle A with the center (2, 0) is transformed to a new point A' (-1, 5) means a circle is shifted to A' with new coordinates.

Therefore transformation done will be A [(2-x), (0-y)]

Here 2 - x = -1

-x = -2 - 1 = -3

x = 3

and 0-y = 5

y = -5

Therefore the transformation done is [(x - 3), (y +5)].

Now we see that the radius of the new circle is changed. Therefore new circle is enlarged with a scale factor of 3/8 = ( new radius/old radius)

So we conclude that a circle A is transformed to A' with [(x -3), (y + 5)]

and then enlarged by a scale factor of 3/8.