To find the coordinates of vertex A' after triangle ABC has been reflected over a vertical line, we need to determine the equation of that vertical line. We know the coordinates of vertex B' (the reflected point of B) are (11, 5).
Vertex B is at B(-5, 5). The reflection of a point across a vertical line can be found by measuring the horizontal distance to the line of reflection and then adding that distance in the opposite direction.
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Find the horizontal distance from B to the line of reflection:
- The x-coordinate of point B is -5. The x-coordinate of point B' is 11.
- The midpoint between B and B' will lie on the line of reflection.
- The midpoint's x-coordinate is calculated as: \[ \frac{-5 + 11}{2} = \frac{6}{2} = 3 \] Therefore, the line of reflection is the vertical line \( x = 3 \).
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Now, we need to find the reflected coordinates of point A(0, 9). The x-coordinate of A is 0:
- The distance from A to the line of reflection is: \[ |0 - 3| = 3 \]
- To find the reflected x-coordinate A', we subtract this distance from the line of reflection: \[ 3 + 3 = 6 \] So, the x-coordinate of A' is 6.
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The y-coordinate remains unchanged during a reflection over a vertical line. Therefore, the y-coordinate of A' is the same as that of A:
- The y-coordinate of A is 9.
Thus, the coordinates of vertex A' are \( (6, 9) \).
Put together, the coordinates of vertex A' are: \[ (6, 9) \]