To find the coordinates of vertex A' after triangle ABC has been reflected over a vertical line, we first need to determine the line of reflection. We know that point B is reflected to point B'.
The reflection of point B(-5, 5) to point B' (11, 5) occurs horizontally. Therefore, the vertical line of reflection must be midway between points B and B'.
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Calculate the midpoint (M) between B and B': \[ M_x = \frac{B_x + B'_x}{2} = \frac{-5 + 11}{2} = \frac{6}{2} = 3 \] \[ M_y = \frac{B_y + B'_y}{2} = \frac{5 + 5}{2} = 5 \] So the midpoint M is (3, 5).
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The line of reflection has the x-coordinate of 3. This means it is the line \( x = 3 \).
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To find A' from A, we apply the reflection across this line:
- The x-coordinate of A (0, 9) is reflected over the line \( x = 3 \).
- The distance from A to the line (3) is: \[ \text{Distance} = 3 - 0 = 3 \]
- Since reflections are equal distances on both sides of the line, the x-coordinate of A' would be: \[ A'_x = 3 + \text{Distance} = 3 + 3 = 6 \]
- The y-coordinate remains unchanged since it is a vertical reflection. Thus, the y-coordinate of A' is the same as A's: \[ A'_y = 9 \]
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Therefore, the coordinates of vertex A' are \( \boxed{(6, 9)} \).