1. **State the problem:** We are given the midpoint $M(-4,4)$ of the line segment $\overline{AB}$ and one endpoint $A(-6,1)$. We need to find the coordinates of the other endpoint $B(x,y)$. 2. **Formula used:** The midpoint formula for a segment with endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$ is $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ This means the midpoint coordinates are the averages of the corresponding coordinates of the endpoints. 3. **Apply the formula:** Given $M(-4,4)$ and $A(-6,1)$, let $B = (x,y)$. Then $$-4 = \frac{-6 + x}{2}$$ $$4 = \frac{1 + y}{2}$$ 4. **Solve for $x$:** Multiply both sides of the first equation by 2: $$-8 = -6 + x$$ Add 6 to both sides: $$x = -8 + 6 = -2$$ 5. **Solve for $y$:** Multiply both sides of the second equation by 2: $$8 = 1 + y$$ Subtract 1 from both sides: $$y = 8 - 1 = 7$$ 6. **Final answer:** The coordinates of point $B$ are $$\boxed{(-2,7)}$$