Question

The equation to the line bisecting the segment joining $(3,-4)$ and $(5,2)$, and having its intercepts on the x-axis and the y-axis in the ratio $2:1$, is

• A. $x+y-3=0$
• B. $2x-y=9$
• C. $x+2y=2$
• D. $2x+y=7$

Answer 1

Answer: (C)

$x+2y=2$

The line passes through $(\frac{3+5}{2},\frac{-4+2}{2})=(4,-1)$.
The equation of line in intercept form
$\frac{x}{2a}+\frac{y}{a}=1$
Now, this pass through $(4,-1).$
$\frac{4}{2a}-\frac{1}{a}=1\Rightarrow \frac{1}{a}=1$
$\Rightarrow a=1$
$\frac{x}{2}+\frac{y}{1}=1$
$x+2y=2$
Hence, option C is the correct answer.