Question

If the point $(5,2)$ bisects the intercept of a line between the axes, then its equation is

• A. $5x+2y=20$
• B. $2x+5y=20$
• C. $5x-2y=20$
• D. $2x-5y=20$

Answer 1

The correct option is B

$2x+5y=20$

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

$(\frac{a}{2},\frac{b}{2})$

According to the question :

$(\frac{a}{2},\frac{b}{2})=(5,2)$

$\Rightarrow \frac{a}{2}=5,\frac{b}{2}=2$

$\Rightarrow a=10,b=4$

The equation of the required line is given below :

$\frac{x}{10}+\frac{y}{4}=1$

$\Rightarrow 2x+5y=20$