If the point (5, 2) bisects the intercept of a line between the a… - Vidyadip

MCQ

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

A
5x + 2y = 20
✓
2x + 5y = 20
C
5x - 2y = 20
D
2x - 5y = 20

✓

Answer

Correct option: B.

2x + 5y = 20

Let the equation of the line be $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$
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 $\Big(\frac{\text{a}}{2},\frac{\text{b}}{2}\Big)$
According to the question:
$\Big(\frac{\text{a}}{2},\frac{\text{b}}{2}\Big)=(5,2)$
$\Rightarrow\frac{\text{a}}{2}=5,\frac{\text{b}}{2}=2$
$\Rightarrow\text{a}=10,\text{b}=4$
The equation of the required line is given below:
$\frac{\text{x}}{10}+\frac{\text{y}}{4}=1$
$\Rightarrow2\text{x}+5\text{y}=20$

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