anonymous
  • anonymous
I need help with this question...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Prove that the two circles shown below are similar.
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anonymous
  • anonymous
i keep seeing these and am totally confused aren't all circles similar?
anonymous
  • anonymous
|dw:1440510136349:dw| notice that E was moved to C so now we have a dilation of \[\huge \frac{ r_1 }{ r_2 }\] which gives the scale factor.

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anonymous
  • anonymous
yes, you need to use a formula to move one over another and dilate it, but idk the formula
anonymous
  • anonymous
Sorry about using the same color, but essentially just using a transformation this actually proves all circles are similar to each other.
anonymous
  • anonymous
so, what formula would i use to translate it?
anonymous
  • anonymous
I mean we could say \[\pi = \frac{ C }{ 2r }\] making all circles the same
anonymous
  • anonymous
and would the scale factor be 3/4?
anonymous
  • anonymous
4/3
anonymous
  • anonymous
ohh, alright
anonymous
  • anonymous
So the trick here is knowing that translations and dilations are the same hence all circles are the same
anonymous
  • anonymous
i found a new formula for translations
anonymous
  • anonymous
\[(x - h){^2} + (y - k){^2} = r{^2}\]
anonymous
  • anonymous
That's the equation of a circle
anonymous
  • anonymous
oh
anonymous
  • anonymous
You may use it though
anonymous
  • anonymous
ok so how would i put this into words? each step i mean
mathmate
  • mathmate
Perhaps try this: given circle E : (x-4)^2+(y-9)^2=3^2 h=-7, k=-8, scale factor = 4/3 so (x-4+7)^2+(y-9+8)=(3*(4/3))^2 gives (x+3)^2+(y-1)^2=4^2 which is the circle C
anonymous
  • anonymous
\[(x,y) \implies (x-h,y-k)\] and end up doing a dilation
anonymous
  • anonymous
ok thanks you guys, i have more questions i'll post in a couple of minutes, i'd appreciate it if you could help me with those as well :)

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