To determine the line of reflection for the point \( T(2, 3) \) reflecting to \( T'(2, -5) \), we first need to find the midpoint between points \( T \) and \( T' \).
The midpoint \( M \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting \( T(2, 3) \) and \( T'(2, -5) \):
\[ M = \left( \frac{2 + 2}{2}, \frac{3 + (-5)}{2} \right) = \left( \frac{4}{2}, \frac{-2}{2} \right) = (2, -1) \]
The line of reflection is always perpendicular to the line joining the original and reflected points and passes through the midpoint \( M(2, -1) \).
Now we can determine the components of the midpoint and the initial and reflected points:
- The x-coordinates of both points \( T \) and \( T' \) are the same, which is \( 2 \).
- The y-coordinates change from \( 3 \) to \( -5 \) (a vertical reflection).
Since the line of reflection maintains the x-coordinate and affects the y-coordinates, the line of reflection must be horizontal.
Furthermore, since the midpoint has a y-coordinate of \(-1\) and is positioned between the two y-coordinates of points \( T \) and \( T' \), the line of reflection must be \( y = -1 \).
Thus, the correct choice is:
The line of reflection is \( y = -1 \).