1. **State the problem:** We are given the midpoint $M(6.5, 11)$ of segment $\overline{KL}$ and one endpoint $L(13, 16)$. We need to find the coordinates of the other endpoint $K$. 2. **Formula for midpoint:** The midpoint $M$ of a segment with endpoints $K(x_1, y_1)$ and $L(x_2, y_2)$ is given by: $$ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) $$ 3. **Apply the formula:** We know $M(6.5, 11)$ and $L(13, 16)$, so: $$ 6.5 = \frac{x_1 + 13}{2} \quad \text{and} \quad 11 = \frac{y_1 + 16}{2} $$ 4. **Solve for $x_1$:** Multiply both sides by 2: $$ 2 \times 6.5 = x_1 + 13 $$ $$ 13 = x_1 + 13 $$ Use cancellation to isolate $x_1$: $$ 13 = x_1 + \cancel{13} \implies x_1 = 13 - 13 = 0 $$ 5. **Solve for $y_1$:** Multiply both sides by 2: $$ 2 \times 11 = y_1 + 16 $$ $$ 22 = y_1 + 16 $$ Use cancellation to isolate $y_1$: $$ 22 = y_1 + \cancel{16} \implies y_1 = 22 - 16 = 6 $$ 6. **Final answer:** The coordinates of point $K$ are: $$ K = (0, 6) $$