A (-3,1)

To find the coordinates of point A after the dilation, we can use the formula for dilation:

\[ P' = O + k \cdot (P - O) \]

where:

• \( P' \) is the new point after dilation.
• \( O \) is the center of dilation.
• \( P \) is the original point.
• \( k \) is the magnitude of dilation.

In this case:

• The center of dilation \( O \) is at (-2, -1).
• The original point \( A \) is at (-3, 1).
• The magnitude of dilation \( k \) is 2.

First, we calculate \( P - O \):

\[ P - O = (-3, 1) - (-2, -1) = (-3 + 2, 1 + 1) = (-1, 2) \]

Next, we multiply this vector by the dilation factor \( k = 2 \):

\[ k \cdot (P - O) = 2 \cdot (-1, 2) = (-2, 4) \]

Now, we add this result to the center of dilation \( O \):

\[ P' = O + k \cdot (P - O) = (-2, -1) + (-2, 4) = (-2 - 2, -1 + 4) = (-4, 3) \]

Thus, the coordinates of the corresponding point \( A' \) after dilation are (-4, 3).

The correct answer is:

a. (-4, 3)