Mathematics Question from JEE Main 2023 · 11 April, Shift 1

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