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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 $\text{ABC}$

1. $\dfrac{25}{16} \\$
2. $\dfrac{16}{9} \\$
3. $\dfrac{32}{19} \\$
4. $\dfrac{40}{23}$

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