Question

According to these three facts, which statements are true?

Circle W has center (−3, 0) and radius 8.
Circle V is a translation of circle W, 2 units down.
Circle V is a dilation of circle W with a scale factor of 2.


Select each correct answer. (You can choose more than one).

A. Circle V and circle W are similar.

B. Circle V and circle W have the same center.

C. The radius of circle V is 16.

D. The center of circle V is (−5, 0).

Answer 1

we have that

1)Circle W has center (−3, 0) and radius 8
the equation of a circle W is
(x+3)²+(y)²=8²

2)Circle V is a translation of circle W, 2 units down.
the center of circle V--------> (-3,0-2)---------> (-3,-2)

3)Circle V is a dilation of circle W with a scale factor of 2.
then the radius circle V is 8*2------> 16 units
the equation of a circle V is
(x+3)²+(y+2)²=16²

therefore

case A. Circle V and circle W are similar.---------> is correct
because I can transform circle V to circle W using only translations, rotations and scaling (In the case of circles, no rotations are necessary).

case B. Circle V and circle W have the same center.-------> is not correct

case C. The radius of circle V is 16.-----------> is correct

case D. The center of circle V is (−5, 0).----------> is not correct


the answer is
case A. Circle V and circle W are similar.---------> is correct
case C. The radius of circle V is 16.-----------> is correct