The point $A$ divides the line segment joining the points $(-\mathrm{5,1})$ and $\left(\mathrm{3,5}\right)$ in the ratio $k:1$ internally and the coordinates of points $B$ and $C$ are $\left(\mathrm{1,5}\right)$ and $\left(7,-2\right)$ respectively. If the area of $∆ABC$ is $2$ sq. units, then the sum of all the values of $k$ is equal to

• A

  $\frac{32}{9}$
• B

  $7$
• Correct answer
  C

  $\frac{94}{9}$
• D

  $\frac{31}{9}$

Hence, the correct answer is option: 'C'.