To reflect a point across a horizontal line \(y = k\), you can use the formula:
\[ Y' = (x, 2k - y) \]
In this case, the point \(Y\) has coordinates \((4, 3)\) and the horizontal line is \(y = 1\).
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Identify the \(y\)-coordinate of the point and the line:
- \(y\) of point \(Y\) is \(3\)
- \(k\) (the line) is \(1\)
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Plug these values into the formula: \[ Y' = (4, 2 \cdot 1 - 3) \] \[ Y' = (4, 2 - 3) \] \[ Y' = (4, -1) \]
Thus, the coordinates of \(Y'\) after reflection are \((4, -1)\).
So the answer is: \(Y' (4, -1)\)