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

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)