To find the coordinates of \(B'\) after the translation, we first need to determine the translation vector. We know the original coordinates of point \(A\) and the new coordinates of point \(A'\):
- Original coordinates of \(A\): \((-5, 4)\)
- New coordinates of \(A'\): \((-6, 8)\)
The translation vector can be determined by subtracting the coordinates of \(A\) from the coordinates of \(A'\):
\[ \text{Translation vector} = A' - A = (-6, 8) - (-5, 4) = (-6 + 5, 8 - 4) = (-1, 4) \]
Now we apply this translation vector to point \(B\):
- Original coordinates of \(B\): \((-1, 4)\)
Calculating the new coordinates of \(B'\):
\[ B' = B + \text{Translation vector} = (-1, 4) + (-1, 4) = (-1 - 1, 4 + 4) = (-2, 8) \]
Therefore, the coordinates of \(B'\) are:
\[ \boxed{(-2, 8)} \]
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