Question

circle b is a transformation of circle a. describe the transformations that show why circle a is similar to circle b. circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of $\frac{5}{4}$, then translating the image 12 units down. circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of $\frac{4}{5}$, then reflecting the image in the y - axis. circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of $\frac{4}{5}$, then rotating the image $180^{circ}$. circle b is the result of dilating circle a with a as the center of dilation and using a scale factor of $\frac{4}{5}$, then translating the image 12 units down.

Explanation:

First, observe Circle A and Circle B on the grid: Circle A is smaller than Circle B? No, wait—Circle A (top) has a radius of 4 units (from center (6,6) to edge (2,6) is 4 units), Circle B (bottom) has a radius of 5 units (from center (6,-6) to edge (2,-6) is 4? Wait correction: Center A is (6,6), distance to right edge (10,6) is 4, so radius 4. Center B is (6,-6), distance to right edge (11,-6) is 5? No, scale factor: Circle B is larger? Wait no, the options have scale factors 5/4 or 4/5. The vertical distance between centers A(6,6) and B(6,-6) is 12 units down. Dilating with center A: if scale factor is 5/4, radius becomes 4*(5/4)=5 (matches Circle B's radius). Then translating 12 units down moves the dilated circle from center A(6,6) to (6,6-12)=(6,-6), which is center B. The other options: reflection/rotation don't change vertical position; scale factor 4/5 makes it smaller (wrong); translation 12 down is correct only with scale factor 5/4.

Answer:

Circle B is the result of dilating Circle A with A as the center of dilation and using a scale factor of $\frac{5}{4}$, then translating the image 12 units down.