To determine the line of reflection that maps point \( T(2, 3) \) to point \( T'(2, -5) \), we can use the property of reflection.
In a reflection, the line of reflection is the perpendicular bisector of the segment connecting the original point and its image.
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Calculate the midpoint of points \( T(2, 3) \) and \( T'(2, -5) \): \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] \[ = \left( \frac{2 + 2}{2}, \frac{3 + (-5)}{2} \right) = \left( 2, \frac{-2}{2} \right) = (2, -1) \]
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Determine the slope of the segment from \( T \) to \( T' \): \[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 3}{2 - 2} = \frac{-8}{0} \text{ (undefined slope, vertical line)} \]
Since the segment connecting \( T \) and \( T' \) is vertical, the line of reflection must be horizontal, which means it will have a constant y-value equal to the y-coordinate of the midpoint.
Thus, the line of reflection is: \[ y = -1 \]
Therefore, the correct answer is: The line of reflection is \( y = -1 \).