URGENTTTTTTT!!!!!!!!!!Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.

Answer:Circle A and circle B are similarStep-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