Subjects algebra

Midpoint Finding 0Afb42

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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 $$\boxed{(-4, -7)}$$