Maximal Trigonal Area

You are given $N$ distinct points $(P_{1, x}, P_{1, y}), (P_{2, x}, P_{2, y}), \dots, (P_{N, x}, P_{N, y})$ on the coordinate plane, and $Q$ queries in the form `L R X`. In each query, consider the polygon formed by the points in the interval $[L,R]$ (i.e. the points $(P_{L, x}, P_{L, y}), (P_{L+1, x}, P_{L+1, y}), \dots, (P_{R, x}, P_{R, y})$), along with $(0,0)$ and $(X,0)$. - If this polygon