prove that circle a with center (–1, 1) and radius 1 is similar to circle b with center (–3, 2) and radius 2.

Circle A and circle B are similar

Step-by-step explanation:

* Lets explain similarity of circles

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

 reflections, translations, rotations, dilations can be found that map one

 figure onto another

- To prove all circles are similar, a translation and a scale factor from a

  dilation will be found to map one circle onto another

* Lets solve the problem

∵ Circle A has center (-1 , 1) and radius 1

∵ The standard form of the equation of the circle is:

   (x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center

   and r is the radius

∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²

∴ Equation circle A is (x + 1)² + (y - 1)² = 1

∵ Circle B has center (-3 , 2) and radius 2

∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²

∴ Equation circle B is (x + 3)² + (y - 2)² = 4

- By comparing between the equations of circle A and circle B

# Remember:

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ -3 - -1 = -2 and 2 - 1 = 1

∴ The center of circle A moves 2 units to the left and 1 unit up to

  have the same center of circle B

∴ Circle A translate 2 units to the left and 1 unit up

∵ The radius of circle A = 1 and the radius of circle B = 2

∴ Circle A dilated by scale factor 2/1 to be circle B

∴ Circle B is the image of circle A after translation 2 units to the left

  and 1 unit up followed by dilation with scale factor 2

- By using the 2nd fact above

∴ Circle A and circle B are similar

the answer

b. they are parallel and will never intersect.

i don't know, but that looks pretty bad. my school passed us unless we failed in all the subjects, but idk abt ur school's rules.

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