Question

If the intercept made by the line between the axis is bisected at the point $\left(5,2\right)$, 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

$2x+5y=20$

Explanation for the correct option:

Let us assume that the $x-$intercept is $\left(a,0\right)$ and $y-$intercept is $\left(0,b\right)$.

Thus, the equation of the straight line can be given by $\frac{x}{a}+\frac{y}{b}=1$.

The midpoint of $\left(a,0\right)$ and $\left(0,b\right)$ can be given by $\left(\frac{a+0}{2},\frac{0+b}{2}\right)=\left(5,2\right)$.

$\Rightarrow \left(\frac{a}{2},\frac{b}{2}\right)=\left(5,2\right)$.

So, either $\frac{a}{2}=5$ or $\frac{b}{2}=2$.

Thus, either $a=10$ or $b=4$.

Therefore, the equation of the straight line, $\frac{x}{a}+\frac{y}{b}=1$.

$$\begin{gathered} \Rightarrow \frac{x}{10}+\frac{y}{4}=1 \\ \Rightarrow \frac{2x+5y}{20}=1 \\ \Rightarrow 2x+5y=20 \end{gathered}$$

Hence, option (B) is the correct answer.