1. **State the problem:** We are given the midpoint $M(-3,-1)$ of segment $\overline{AB}$ and one endpoint $A(-2,5)$. We need to find the coordinates of the other endpoint $B(x,y)$.
2. **Formula used:** The midpoint $M$ of a segment with endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by
$$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$
This means
$$-3 = \frac{-2 + x}{2} \quad \text{and} \quad -1 = \frac{5 + y}{2}$$
3. **Solve for $x$:**
Multiply both sides by 2:
$$-6 = -2 + x$$
Add 2 to both sides:
$$x = -6 + 2 = -4$$
4. **Solve for $y$:**
Multiply both sides by 2:
$$-2 = 5 + y$$
Subtract 5 from both sides:
$$y = -2 - 5 = -7$$
5. **Final answer:** The coordinates of point $B$ are
$$\boxed{(-4, -7)}$$
Midpoint Finding 0Afb42
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