Question

Which transformations can be used to show that circle S is similar to circle T?

Circle S: center (11, −5) and radius 81

Circle T: center (11, 0) and radius 9



Select each correct answer.

Circle S is congruent to circle T.

Circle S is a translation of circle T, 5 units down.

Circle S is a dilation of circle T with a scale factor of 72.

Circle S is a dilation of circle T with a scale factor of 9.

Answer 1

The answers are B and C.

I'm sorry I can't explain why but I just took the test and got the answers right, so... Also, Lemme recommend Desmos Graphing Calculator for a minute cause all I have to do is type in the equation and count from there. The graphing calculator is your friend. Embrace it.

Answer 2

Options (2) and (4) are the correct options.

Transformation rules:

• If a point (h, k) is translated by 'a' units down, rule for the transformation will be,

        (h, k) → (h, k-a)

• If a segment is dilated by a scale factor 'k', length of the segment will be,

    Length of the image = k(length of the preimage or original segment)

Apply these rules,

If the center (11, 0) of a circle T is translated to the center (11, -5) of circle S,

(11, 0) → (11, 0-5)

Therefore, circle T is translated by 5 units down.

If the circle T is dilated by a scale factor 'k' to form the image circle S

Radius of the image circle S = k(radius of the preimage circle T)

81 = k(9)

k = $\frac{81}{9}$

k = 9

Therefore, circle T is dilated to form the image circle S with a scale factor 9.

     Hence, Options (2) and (4) are the correct options.

Learn more about the transformations here,

https://brainly.com/question/2856466?referrer=searchResults