The line $\text{L}$ passing through the points $(1,1)$ and $(2,0)$ meets the $y$-axis at $\text{A}$. The line through the point $\left(\dfrac{1}{2},0 \right)$ and perpendicular to $\text{L}$ meets the $y$-axis at $\text{B}$ and $\text{L}$ at $\text{C}$. Find area of the triangle $\text{ABC}$
- $\dfrac{25}{16} \\$
- $\dfrac{16}{9} \\$
- $\dfrac{32}{19} \\$
- $\dfrac{40}{23}$