To reflect the point \( Y(4, 3) \) across the horizontal line \( y = 1 \), we need to determine the distance of point \( Y \) from the line and then find the point at the same distance on the opposite side.
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Find the vertical distance from point \( Y \) to the line \( y = 1 \):
The \( y \)-coordinate of point \( Y \) is \( 3 \). The line is at \( y = 1 \).
The distance from \( Y \) to the line is: \[ 3 - 1 = 2 \]
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Reflect over the line by going the same distance below the line: To find the reflected point \( Y' \), we subtract the distance from the line: \[ y' = 1 - 2 = -1 \]
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The \( x \)-coordinate remains the same (since it is a horizontal reflection): Therefore, the coordinates of point \( Y' \) will be: \[ Y' = (4, -1) \]
So the coordinates of \( Y' \) after reflection across the line \( y = 1 \) are \( (4, -1) \).