1. **State the problem:** We are given the midpoint $M(2.5, -6.5)$ of segment $\overline{PQ}$ and one endpoint $P(-5, -15)$. We need to find the coordinates of the other endpoint $Q(x, y)$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 3. **Apply the formula:** We know $M(2.5, -6.5)$ and $P(-5, -15)$, so: $$2.5 = \frac{-5 + x}{2}$$ $$-6.5 = \frac{-15 + y}{2}$$ 4. **Solve for $x$:** Multiply both sides by 2: $$2 \times 2.5 = -5 + x$$ $$5 = -5 + x$$ Add 5 to both sides: $$5 + 5 = \cancel{-5} + x + 5$$ $$10 = x$$ 5. **Solve for $y$:** Multiply both sides by 2: $$2 \times (-6.5) = -15 + y$$ $$-13 = -15 + y$$ Add 15 to both sides: $$-13 + 15 = \cancel{-15} + y + 15$$ $$2 = y$$ 6. **Final answer:** The coordinates of the other endpoint $Q$ are: $$Q = (10, 2)$$