To determine the coordinates of point B' after the translation, we first need to analyze the translation vector based on the change from point A to point A'.
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Identify the coordinates of point A and A':
- Point A: (-3, 2)
- Point A': (-6, 8)
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Calculate the translation vector: To find the translation vector, we calculate the change in the x and y coordinates:
- Change in x: x' - x = -6 - (-3) = -6 + 3 = -3
- Change in y: y' - y = 8 - 2 = 6
- Thus, the translation vector \( \vec{T} \) is (-3, 6).
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Apply the translation vector to point B: Now, we apply this translation vector to point B to find point B'.
- Coordinates of B: (-1, 2)
- Apply the translation:
- New x-coordinate: -1 + (-3) = -1 - 3 = -4
- New y-coordinate: 2 + 6 = 8
- Therefore, the coordinates of B' are (-4, 8).
So, the coordinates of B' are \(\boxed{(-4, 8)}\).
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