To find the coordinates of B' after applying a translation vector to rectangle ABDC, we need to determine the translation vector that was applied.
The original coordinates of points A and B are as follows:
- A = (-5, 4)
- B = (-1, 4)
We know that the new coordinates of A' upon translation are A' = (-6, 8).
To determine the translation vector, we can find the change in the x and y coordinates from A to A':
\[ \text{Translation vector} = (A'_x - A_x, A'_y - A_y) = (-6 - (-5), 8 - 4) = (-1, 4). \]
This means we translate each point by (-1, 4).
Now we apply this translation vector to point B: \[ B' = B + \text{Translation vector}. \] \[ B' = (-1, 4) + (-1, 4) = (-1 - 1, 4 + 4) = (-2, 8). \]
Thus, the coordinates of B' are (-2, 8).
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