Answer:
Circle A and circle B are similar
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