Question

Circle A has center of (2, 3) and a radius of 5. Circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B?

Answer 1

Dilate circle A by a scale factor of 2.

Translate circle A using the rule (x+1, y−1).

Rotate circle A 180° about the center.

Reflect circle A over the y-axis.

Answer 2

\(\normalsize\color{blue}{ (x-h)^2+(y-k)^2=r^2 }\) where `r - radius` and `(h,k) is the center` .

Answer 3

dilating the circle by a scale factor of `c` means to multiply the radius times c.

Answer 4

If something is troubling you, tell me what is it?

Answer 5

okay, So would that mean the answer is choice A? @SolomonZelman

Answer 6

Wel, you DID dilate the circle by a scale factor of 2, but you ALSO moved the center from (2,3) to (1,4)

Answer 7

So the center is moved using the rule (x-1,y+1) and the circle is dilated by a scale factor of 2.
(The order doesn't matter, since bboth ways the result is same)

Answer 8

oh so it would be B?@SolomonZelman

Answer 9

I think you have a type in the rule in option B

Answer 10

I copied and pasted the choices and I just checked there is not a typo. @SolomonZelman

Answer 11

Well, comparing the original center (2,3) and the obtained one (1,4) you can see that you go
(x-1,y+1) `[ and not (x+1,y-1) ]` , right ?

Answer 12

Right. But I am confused is it not B?

Answer 13

well, if you go backwards from circle B to circle A, then you can say that the rule is (x+1,y-1)

as (4 , 1)
\(\normalsize\color{blue}{~^{-1} }\) \(\normalsize\color{blue}{~^{+1} }\)
as (3 , 2)

see ?

Answer 14

So if you say this rule from B to A (not the opposite way), then the rule is right.

Answer 15

oh ok that's sense

Answer 16

Well, then it is A and B, right ?

Answer 17

it's B @SolomonZelman

Answer 18

A and B

Answer 19

Well obviously can't be A and B so... going elsewhere :(

Answer 20

did you ever find out what is was?? @truffles

Answer 21

Its A, If you use B, think about it, 2,3 + (1,-1), does that give you 1,4, NO