Answer
Option A is correct.
(x, y) → (x + 9, y - 2); D₃
Step-by-step explanation
When a coordinate A(x, y) is translated horizontally along the x-axis by a units, the new coordinates, A'(x', y') is represented as
A[(x + a), y] when the translation is by a units to the right.
A[(x - a), y] when the translation is by a units to the left.
When a coordinate A(x, y) is translated vertically along the y-axis by b units, the new coordinates, A'(x', y') is represented as
A' [x, (y + b)] when the translation is by b units upwards.
A [x, (y - b)] when the translation is by b units downwards.
We can see that the coordinates of the center of circle A (-5, 3) becomes the center of circle B (4, 1)
We can easily see that the center of A is moved 9 units to the right and 2 units downwards.
So, the first transformation is
(x, y) → (x + 9, y - 2)
Then, we can see that the radius of the circle A changes from 2 units to 6 units.
That means the circle B is circle dilated by a factor of 3.
So, the total transformation is
(x, y) → (x + 9, y - 2); D₃
Hope this Helps!!!