To find the line of reflection that maps point T(2, 3) to point T′(2, −5), we can use the property that the line of reflection is the perpendicular bisector of the segment connecting the original point and its image.
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First, we find the midpoint of segment TT′:
- Midpoint \( M \) of segment \( TT′ \) can be calculated as: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{2 + 2}{2}, \frac{3 + (-5)}{2} \right) = \left( 2, \frac{3 - 5}{2} \right) = \left( 2, -1 \right) \]
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Next, we determine the slope of the segment \( TT′ \):
- The slope \( m \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 3}{2 - 2} = \frac{-8}{0} \] This indicates that the segment is vertical, as the change in x is 0.
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The line of reflection will be a horizontal line that passes through the midpoint. Since the midpoint is \( M(2, -1) \), the line of reflection is the line \( y = -1 \).
Thus, the correct response is: The line of reflection is \( y = -1 \).