Let the equation of the line be \(\frac{x}{a}+\frac{y}{b} = 1\)
The coordinates of the intersection of this line with the coordinate axes are (a, 0) and (0, b).
The midpoint of (a, 0) and (0, b) is, \(\Big(\frac{a}{2},\frac{b}{2}\Big)\)
According to the question:
\(\Big(\frac{a}{2},\frac{b}{2}\Big)\) = (5,2)
⇒ \(\frac{a}{2}=5,\frac{b}{2}=2\)
⇒ a = 10, b = 4
The equation of the required line is given below:
\(\frac{x}{10}+\frac{y}{4}=1\)
⇒ 2x + 5y = 20
