Question

Prove that the two circles shown below are similar.

Answer 1

@AZ

Answer 2

Well yes, but you must prove it in this question

Answer 3

You're probably learning about transformations in geometry right now, right?

Answer 4

Actually it was a while ago that they went through that

Answer 5

To me this looks a whole lot like a dilation with a translation

Answer 6

exactly, you just show that it was translated and dilated

Answer 7

How do you show that?

Answer 8

You take the center of the circle and compare it to the center of the other circle

So for the smaller circle, it's (0, -1) and the larger one it's (3, 4)

what would it take to translate it from (0, -1) to (3, 4)

Answer 9

3...?

Answer 10

how much do you add the x-values

and y-value

0 + x = 3

-1 + y = 4

Answer 11

you're translating both along the x-axis and the y-axis

Answer 12

Ok :)

Answer 13

What about the dilation?

Answer 14

The larger circle has a radius of 5 and the smaller circle has a radius of 2

To find the dilation, you would have to just divide the two numbers

Answer 15

How would you know to divide the two numbers?

Answer 16

Imagine it like scaling
For example those triangle weird things you have to do, where like you have to find the scale factor
you do that by dividing them by each other
so, same here

Answer 17

Triangle weird things...? What do you mean exactly?

Answer 18

Those things where you find 2 triangles are similar, you see that the angles are the same but then the sides are just scaled
or, the things where for example, they give you a triangle, then tell you to dilate it by 3, you dilate it by multiplying each side by 3

Answer 19

Because it's a circle so from the center to any end of the circle is the same length

and so you're dilating the circle so you just divide the radius by each other depending on whether you're making it bigger or smaller

Answer 20

And so, you multiply to get one shape to the other, so you diivde to find out how much it was multiplied

Answer 21

so like dilating by 5/2 if you're enlarging

and 2/5 if you're shrinking

Answer 22

Oh, ok

Answer 23

So what do I put exactly for the evidence that it was dilated?

Answer 24

From the center point to the circle, well, that's radius, and radius is the same wherever point you end it at, like, around the circle, so, well, if the radius multiplied by something gets the bigger circle's radius, that's the scale factor

honestly, circles are just similar..... i don't understand the point... circles are called circles because they are a circle... like, each circle that wherever you find is similar to one another???????!!!!!!!

Answer 25

I dont know thats the question dont kill me please!

Answer 26

Haha you're right though

Answer 27

smh, i would assume your teacher would want you to write a thorough explanation,b ut like
hm
tell your teacher that two circles are just similar._., no two circles aren't, if they aren't similar, one isn't a circle._.

Answer 28

:/ I'm not sure she'll accept that as an answer...

Answer 29

nono, i meant still type out what AZ wrote above, and then write out the explanation about dilation

you can just write that circles are similar in nature as a side note xd

Answer 30

Oh ok! :)