Question

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

पर्याय

•  5x + 2y = 20

•  2x + 5y = 20

• 5x − 2y = 20

•  2x − 5y = 20

Answer 1

 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:

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

$$\Rightarrow 2x+5y=20$$