Let A(1,1), B(-4,3), C(-2,-5) be vertices of a triangle A B C, P be a point on side B C, and Δ_1 and Δ_2 be the areas of triangles A P B and A B C,…

Let $\displaystyle A(1,1), B(-4,3), C(-2,-5)$ be vertices of a triangle $\displaystyle A B C, P$ be a point on side $\displaystyle B C$, and $\displaystyle \Delta_1$ and $\displaystyle \Delta_2$ be the areas of triangles $\displaystyle A P B$ and $\displaystyle A B C$, respectively. If $\displaystyle \Delta_1: \Delta_2=4: 7$, then the area enclosed by the lines $\displaystyle A P, A C$ and the $\displaystyle x$-axis is