Let R be a rectangle given by the lines x=0, x=2, y=0 and y=5. Let A (α, 0) and B (0, β), α ∈[0,2] and β ∈[0,5], be such that the line segment AB…

Let R be a rectangle given by the lines $\displaystyle x=0, x=2, y=0$ and $\displaystyle y=5$. Let $\displaystyle \mathrm{A}(\alpha, 0)$ and $\displaystyle \mathrm{B}(0, \beta), \alpha \in[0,2]$ and $\displaystyle \beta \in[0,5]$, be such that the line segment AB divides the area of the rectangle $\displaystyle R$ in the ratio $\displaystyle 4: 1$. Then, the mid-point of $\displaystyle A B$ lies on a