To find the coordinates of point Z' after a reflection across the line \(y = 1\), we follow these steps:
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Identify the coordinates of point Z: The coordinates of point Z are \((6, 0)\).
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Determine the distance from Z to the line of reflection: The line \(y = 1\) is horizontal and our point Z has a \(y\)-coordinate of 0. The distance from Z to the line \(y = 1\) is: \[ \text{Distance} = 1 - 0 = 1 \]
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Reflect point Z across the line: To find the reflected point Z', we need to move the same distance below the line \(y = 1\) to above the line: \[ \text{New } y\text{-coordinate} = 1 + 1 = 2 \]
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Combine with the original x-coordinate: The x-coordinate remains the same during a reflection across a horizontal line: \[ Z' = (6, 2) \]
So the coordinates of Z' after reflection across \(y = 1\) are \((6, 2)\).
The correct answer from the options provided is: D. Z' (6, 2).