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

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

According to the question:

$$\begin{gathered} \left(\frac{a}{2},\frac{b}{2}\right)=\left(5,2\right) \\ \Rightarrow \frac{a}{2}=5,\frac{b}{2}=2 \\ \Rightarrow a=10,b=4 \end{gathered}$$

The equation of the required line is given below:

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