To find the coordinates of point B' after applying the same translation vector that was applied to point A to obtain A', we first need to determine the translation vector.
The original coordinates of point A are \( A = (-5, 4) \), and the new coordinates after translation are \( A' = (-6, 8) \).
The translation vector \( T \) can be calculated as follows:
\[ T_x = A'_x - A_x = -6 - (-5) = -6 + 5 = -1 \]
\[ T_y = A'_y - A_y = 8 - 4 = 4 \]
Thus, the translation vector is \( T = (-1, 4) \).
Now, we apply this translation vector to point B:
The original coordinates of point B are \( B = (-1, 4) \).
Calculating the new coordinates \( B' \):
\[ B'_x = B_x + T_x = -1 + (-1) = -1 - 1 = -2 \]
\[ B'_y = B_y + T_y = 4 + 4 = 8 \]
So, the coordinates of \( B' \) after the translation are \( B' = (-2, 8) \).
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