1. **State the problem:** We are given the midpoint $M(-17, 6.5)$ of segment $\overline{JK}$ and one endpoint $K(-15, -6)$. We need to find the coordinates of the other endpoint $J$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $J(x_1, y_1)$ and $K(x_2, y_2)$ is given by $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ This means $$-17 = \frac{x_1 + (-15)}{2}$$ $$6.5 = \frac{y_1 + (-6)}{2}$$ 3. **Solve for $x_1$:** Multiply both sides by 2 $$2 \times -17 = x_1 - 15$$ $$-34 = x_1 - 15$$ Add 15 to both sides $$-34 + 15 = x_1$$ $$x_1 = -19$$ 4. **Solve for $y_1$:** Multiply both sides by 2 $$2 \times 6.5 = y_1 - 6$$ $$13 = y_1 - 6$$ Add 6 to both sides $$13 + 6 = y_1$$ $$y_1 = 19$$ 5. **Final answer:** The coordinates of endpoint $J$ are $$J = (-19, 19)$$