Proving circles are similar: Choose any of the transformations that would be a step in proving that Circle A is similar to Circl

Question

2 years ago

10

Proving circles are similar: Choose any of the transformations that would be a step in proving that Circle A is similar to Circl

e C. Select ALL that apply.
A.
Reflect A over the line y=x

B.
Translate C (x+5,y-4)

C.
Dilate A by 3/2

D.
Dilate C by 3/2

E.
Translate A by (x-5, y+4)

Mathematics

1 answer:

Ulleksa [173] · Answer 1 · 2023-07-21T18:33:03+03:00

The transformations that would prove that circles A and C are similar are:

A. Reflect A over the line y=x
C. Dilate A by 3/2

<h3>How to prove that circle A and circle C are similar?</h3>

The circles are given as:

Circle A and B

Assume the following parameters:

The center of circle A is (2,3) with a radius of 2
The center of circle B is (3,2) with a radius of 3

To start with;

The circle A must be reflected across the line y = x with the following transformation rule:

(x,y) -> (y,x)

So, we have:

(2,3) -> (3,2)

Next, the radius of A must be dilated by 3/2 as follows:

New Radius = 3/2 * 2 = 3

After the transformations, we have the following parameters:

The center of circle A is (3,2) with a radius of 3
The center of circle B is (3,2) with a radius of 3

Notice that both circles now have the same center and radius.

Hence, both circles are similar