Question

Circle A has center of (2, 3), and a radius of 5 and 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?

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 1

any help?

Answer 2

Havent used this site in months figured i would give it a whirl.

Answer 3

@jim_thompson5910 @zepdrix

Answer 4

@SolomonZelman @sleepyjess

Answer 5

If you dilate figure A and you're able to match it to figure B (after dilation) then that shows figure A is similar to figure B

For example, these two triangles are similar. The large one has all sides multiplied by the same constant to get the triangle bigger.

http://mathworld.wolfram.com/images/eps-gif/Dilation_900.gif

Answer 6

well i put A? would i be correct?

Answer 7

Especially since you summed it up that way? @jim_thompson5910

Answer 8

yes A is correct

Answer 9

thanks, I may need one more.

Answer 10

A circle is centered at (7, 8) and has a radius of 11. Which of the following is the equation for this circle?

(x − 7)2 + (y − 8)2 = 121
(x − 7)2 + (y − 8)2 = 11
(x + 7)2 + (y + 8)2 = 121
(x + 7)2 + (y + 8)2 = 11
I put c @jim_thompson5910
I am not sure this is correct though honestly becuase none of my research matches this equation. I think I have a broad idea but I cant pin point one.

Answer 11

@sweetburger @SamsungFanBoy

Answer 12

@jabez177

Answer 13

`A circle is centered at (7, 8)`

h = 7
k = 8

(x-h)^2 + (y-k)^2 = r^2
notice how it's x-h and y-k. The negatives in front of h and k tell us to take the opposite

(x-7)^2 + (y-8)^2 = r^2
then you'd plug in the given radius for r

Answer 14

was 7 and 8 the given radius?

Answer 15

no, the radius is given after the center point is given

Answer 16

(7,8) is your center

Answer 17

So we are trying to find the radius? They didn't tell us? If so it could be 11.

Answer 18

yeah they just gave it to you. The radius is 11

Answer 19

if r = 11, then r^2 = ???

Answer 20

121 :)

Answer 21

so was c correct?

Answer 22

go back to my first post

Answer 23

the one where I talk about (x-h)^2+(y-k)^2

Answer 24

(x − 7)2 + (y − 8)2 = 121
^
... was I supposed to change the opposite to this...
v
(x + 7)2 + (y + 8)2 = 121
Or the other way around thats where I am confused.

Answer 25

I thought based on your negtives it would be positives... but now your saying no i think? Idk

Answer 26

Given center is (h,k) = (7,8). Radius is r = 11.

So,

\[\Large {\color{blue}{h = 7}}\]
\[\Large {\color{green}{k = 8}}\]
\[\Large {\color{red}{r = 11}}\]

Plug them into the general circle equation

\[\Large (x-h)^2 + (y-k)^2 = r^2\]

\[\Large (x-{\color{blue}{h}})^2 + (y-{\color{green}{k}})^2 = ({\color{red}{r}})^2\]

\[\Large (x-{\color{blue}{7}})^2 + (y-{\color{green}{8}})^2 = ({\color{red}{11}})^2\]

\[\Large (x-7)^2 + (y-8)^2 = 121\]

Answer 27

oh so it is the negatives ok?

Answer 28

(x − 7)2 + (y − 8)2 = 121

Answer 29

^ like that?

Answer 30

yes but don't say (x-7)2 write (x-7)^2

Answer 31

`^` means exponent

Answer 32

oh i was using that as an arrow.

Answer 33

mb

Answer 34

example

3x^2 = \(\Large 3x^2\)