$M$ is the midpoint of $\overline{A N}, A$ has coordinates $(2,-3)$, and $M$ has coordinates $(5,1)$. Find the coordinates of $N$. $(8,5)$ $(7,-2)$ $\left(9 \frac{1}{2}, 4\right)$ $\left(3 \frac{1}{2},-1\right)$

Step 1 ：Use the midpoint formula: \(M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\)

Step 2 ：Substitute the given values: \(M = \left(\frac{2 + x_2}{2}, \frac{-3 + y_2}{2}\right)\)

Step 3 ：Simplify the equations: \(5 = \frac{2 + x_2}{2}\) and \(1 = \frac{-3 + y_2}{2}\)

Step 4 ：Multiply both sides of the first equation by 2: \(10 = 2 + x_2\)

Step 5 ：Subtract 2 from both sides: \(x_2 = 8\)

Step 6 ：Multiply both sides of the second equation by 2: \(2 = -3 + y_2\)

Step 7 ：Add 3 to both sides: \(y_2 = 5\)

Step 8 ：Therefore, the coordinates of point \(N\) are \((8, 5)\).