To find the coordinates of point \( Z' \) after a reflection across the line \( y = 1 \), we first need to determine the original coordinates of point \( Z \).
Let's assume that the original coordinates of \( Z \) are given as \( (x, y) \). When reflecting a point across a horizontal line, the x-coordinate remains the same, while the y-coordinate is transformed based on its distance to the line of reflection.
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Determine the distance from \( Z \) to the line \( y = 1 \). If \( Z \) is at \( (x, y) \), the distance from point \( Z \) to the line \( y = 1 \) is \( |y - 1| \).
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The reflected point \( Z' \) will be at the same x-coordinate, with the y-coordinate calculated as follows: \[ Z' = (x, 1 - (y - 1)) = (x, 2 - y) \]
Now, if we use a specific original location for \( Z \):
- If \( Z \) is at \( (-4, 2) \): \[ Z' = (-4, 2 - (2 - 1)) = (-4, 0) \]
Thus, the coordinates of \( Z' \) after the reflection across the line \( y = 1 \) would be \( Z'(-4, 0) \).
Therefore, the correct answer is: \[ Z′(-4, 0) \quad \text{(upper Z prime left parenthesis negative 4 comma 0 right parenthesis)} \]