The points $(2,3)$ and $\left(-4,-\frac{4}{3}\right)$ lie on the opposite sides of the line $\mathrm{L} \equiv 5 \mathrm{x}-6 \mathrm{y}+\mathrm{k}=0$ and k is an integer. If the points $(1,2)$ and $(4,5)$ lie on the same side of the line $\mathrm{L}=0$, then the perpendicular distance from origin to the line $\mathrm{L}=0$ is

• A

  $\frac{7}{\sqrt{61}}$
• B

  $\frac{9}{\sqrt{61}}$
• C

  $\frac{10}{\sqrt{61}}$
• Correct answer
  D

  $\frac{11}{\sqrt{61}}$

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