Circle a has a center of (-2,4) and a radius of 4, and circle b has a center of (3,9) and a radius of 8. what steps will show that circle a is similar to circle b?
a) translate circle a using the rule (x-5,y-5)
b)dilate circle a by a scale factor of 2
c)reflect circle a over the x axis
d) rotate circle a 90 degrees clockwise about the center

The steps to prove the two circles are similar are:

Translation, 5 units to the right and 5 units up followed by  Dilation of scale factor 2

Step-by-step explanation:

* Lets explain the similarity in the circles

- Circles can be proven similar if one, or more, similarity transformations

 reflections, translations, rotations, dilation can be found that map

 one circle onto another.

- All circles are similar, if a translation and a scale factor from a dilation

 will be found to map one circle onto another.

- A translation, followed by a dilation with scale factor r2/r1 will map one

 circle onto the other

- The equation of any circle is (x - h)² + (y - k)² = r², where h and k are

 the coordinates of the center of the circle and r is its radius

* Now lats solve the problem

- Circle A has a center of (-2,4) and a radius of 4

∵ (h , k) is the center of the circle and r is its radius

∴ h = -2 and k = 4

∵ r = 4

∴ r² = 4² = 16

∴ (x + 2)² + (y - 4)² = 16 is the equation of the circle A

- Circle B has a center of (3,9) and a radius of 8

∵ (h , k) is the center of the circle and r is its radius

∴ h = 3 and k = 9

∵ r = 8

∴ r² = 8² = 64

∴ (x - 3)² + (y - 9)² = 64 is the equation of the circle B

- From the two equations there are a translation

∵ x-coordinate of circle A is -2

∵ x-coordinate of circle B is 3

∵ 3 - -2 = 5

∴ The x-coordinate of circle A translated 5 units to the right

∵ y-coordinate of circle A is 4

∵ y-coordinate of circle B is 5

∵ 9 - 4 = 5

∴ The y-coordinate of circle A translated 5 units up

∴ Circle A is translated 5 units to the right and 5 units up

- The radius of circle A is 4 and the radius of circle B is 8

∵ r1 = 4 and r2 = 8

∵ r2/r1 = 8/4 = 2

∴ Circle A is dilated by a scale factor of 2

∴ There is translation, 5 units to the right and 5 units up, followed by

  a dilation, of scale factor 2 then the two circles are similar

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