Question

Can someone help me with this problem?

Explain how circle x (-4,9) with radius 8 is similar to circle z (6,3) with radius 11?

Answer 1

have you tried using translations and dialations ?

Answer 2

?

Answer 3

translation is moving the circle
dialations shrinks or enlarges the circle by a scale factor

Answer 4

ok let me try and work it out, could you check my answer when you are done.

Answer 5

we can also use similar triangles

Answer 6

I would use scale factor( k= r2/r1) of 11/8
Then I would move the circle 11 to the right
Then I would move the circle 6 down

Is that right?

Answer 7

to get from x=-4 to x=6 you move right 10 units correct?

Answer 8

correct. sorry over counted

Answer 9

oh i missed a gap on my graph. that is why i miss counted

Answer 10

So you need the translation T(x+10,y-6) to move x(-4,9) to z(6,3)
This says we are moving (-4,9) right 10 units and 6 units down to get (6,3)
then yes use the dilation 11/8 to get the circles to lay on top each other looking as if there is only one circle but there is really two one laying on the other

Answer 11

you have proved the circles are similar by doing this

Answer 12

Thank you so much! that makes sense.

Answer 13

we will use the dilation on the smaller circle by the way

Answer 14

11/8 ( the radius of the small circle )=11/8 (8)=11 which is the radius of the bigger circle

Answer 15

anyways good job

Answer 16

also I spelled dilation wrong earlier
i wrote dialation

Answer 17

oh ok. thank you so much!