1. **State the problem:** We are given the midpoint $M(6.5, 3.5)$ of segment $\overline{RS}$ and one endpoint $S(15, -12)$. We need to find the coordinates of the other endpoint $R(x, y)$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $R(x, y)$ and $S(x_2, y_2)$ is given by: $$ M = \left( \frac{x + x_2}{2}, \frac{y + y_2}{2} \right) $$ 3. **Apply the formula:** Substitute $M(6.5, 3.5)$ and $S(15, -12)$: $$ 6.5 = \frac{x + 15}{2} \quad \text{and} \quad 3.5 = \frac{y + (-12)}{2} $$ 4. **Solve for $x$:** Multiply both sides by 2: $$ 2 \times 6.5 = x + 15 $$ $$ 13 = x + 15 $$ Subtract 15 from both sides: $$ 13 - \cancel{15} = x + \cancel{15} $$ $$ x = -2 $$ 5. **Solve for $y$:** Multiply both sides by 2: $$ 2 \times 3.5 = y - 12 $$ $$ 7 = y - 12 $$ Add 12 to both sides: $$ 7 + \cancel{12} = y - \cancel{12} $$ $$ y = 19 $$ 6. **Final answer:** The coordinates of the other endpoint $R$ are: $$ R = (-2, 19) $$