To find the coordinates of point \( S \), given that point \( T \) has coordinates \( (0, 2) \) and the midpoint \( M \) of segment \( \overline{ST} \) is \( (1, -5) \), we can use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, \( M \) is the midpoint, \( (x_1, y_1) \) is the coordinate of point \( S \), and \( (x_2, y_2) \) is the coordinate of point \( T \) which is \( (0, 2) \).
Let the coordinates of point \( S \) be \( (x, y) \). According to the midpoint formula:
\[ (1, -5) = \left( \frac{x + 0}{2}, \frac{y + 2}{2} \right) \]
We can set up two equations based on this:
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For the x-coordinates: \[ 1 = \frac{x + 0}{2} \implies 2 = x \implies x = 2 \]
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For the y-coordinates: \[ -5 = \frac{y + 2}{2} \implies -10 = y + 2 \implies y = -12 \]
Thus, the coordinates of point \( S \) are \( (2, -12) \).
The other endpoint is: \[ \boxed{(2, -12)} \]