Circle C with center at (−4, 6) and radius 2 is similar to circle D with center at (6, −2) and radius 4. Below is an incorrect informal argument for proving two circles are similar:

If we move circle C's center ten units to the right and eight units down, the new center would be at (-4 + 10), (6 - 8) = (6, -2). So step 1 in the informal proof checks out - the centers are the same (which is the definition of concentric) and the shifts are right.

Let's look at our circles. Circle C has a radius of 2 and is inside circle D, whose radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio, as seen below:

[tex] \frac{1}{2} = \frac{radius--circle C}{radius--circle D} [/tex]

If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. The second step checks out.

Translated objects (or those that you shift) can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.

Thus, the argument is correct and the last choice is best.

swapnalimalwadeVT swapnalimalwadeVT · Answer 2 · 2022-03-19T11:20:49+01:00

We are told that circle C has center (-4, 6) and a radius of 2.

is similar to circle D has center (6, -2) and a radius of 4.

What is the similar circles?

They have the same shape, but not necessarily the same size

The argument is correct and the last choice is best.

By given conditions we have,

When we move circle C's center ten units to the right and eight units down, the new center would be at

(-4 + 10), (6 - 8) = (6, -2).

Therefore step 1 in the informal proof is the centers are the same (which is the definition of concentric) and the shifts are right.

Now next, our circles. Circle C has a radius of 2 and is inside circle D,has radius is 4. Between Circle C and Circle D, the radii have a 1:2 ratio,

If we dilate circle C by a factor of 2, it means we are expanding it and doubling it. Our circle has that 1:2 ratio, and doubling both sides gives us 2:4. Therefore second step is correct.

Translated objects can be congruent, and dilated objects are used with similarity (where you stretch and squeeze). The third step checks out.

Thus, the argument is correct and the last choice is best.

To learn more about the similar circle visit:

https://brainly.com/question/24756209