Given that $M(2,5)$ is the midpoint of $\overline{AB}$ and $A(3,1)$ is one endpoint, what is the product of the coordinates of point $B$?
To find the coordinates of point $B$, I need to use the fact that the midpoint of a line segment is the average of the endpoints. That means that the x-coordinate of $M$ is the average of the x-coordinates of $A$ and $B$, and the same for the y-coordinates. So I can write two equations: $2 = \frac{3 + x_B}{2}$ and $5 = \frac{1 + y_B}{2}$. Solving for $x_B$ in the first equation, I get $x_B = 2 \times 2 - 3 = 1$. Solving for $y_B$ in the second equation, I get $y_B = 2 \times 5 - 1 = 9$. Therefore, the coordinates of $B$ are $(1,9)$. To find the product of the coordinates, I just multiply them: $1 \times 9 = 9$. 