To find the coordinates of \( B' \) using the same translation that maps point \( A (-5, 13) \) to point \( A' (2, 9) \), we need to determine the translation vector.
The translation vector can be found by calculating the difference in coordinates between \( A' \) and \( A \):
\[ \text{Translation vector} = A' - A = (2 - (-5), 9 - 13) = (2 + 5, 9 - 13) = (7, -4) \]
Now, we apply this translation vector to point \( B (4, -2) \) to find the coordinates of \( B' \):
\[ B' = B + \text{Translation vector} = (4, -2) + (7, -4) = (4 + 7, -2 - 4) = (11, -6) \]
Thus, the coordinates of \( B' \) would be \( (11, -6) \).