Question

Sol. [Key Concept: Least area of a lattice quadrilateral (shoelace / Pick) is $\frac{1}{2}$.]

Area of $ABCD = mod$ of

$$\begin{matrix} \frac{1}{2}\left| \begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{4} & y_{4} & 1 \end{matrix} \right| + mod\text{~}\text{of}\text{~}\frac{1}{2}\left| \begin{matrix} x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \\ x_{4} & y_{4} & 1 \end{matrix} \right| \\ \end{matrix} \geq \frac{1}{2}(1) + \frac{1}{2}(1) = 1$$