Question

What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?

• A. $2x-y=4$
• B. $2x-y+4=0$
• C. $2x+y=4$
• D. $2x+y+4=0$

Answer 1

Answer: (C)

$2x+y=4$

Let the equation of the line be $y=mx+c$, now the point at which the line intersects X-axis be $(a,0)$, and the point at which it intersects Y-axis be $(0,b)$

$\Rightarrow m\times a+c=0$

$\Rightarrow a=-\frac{c}{m}$

and $b=c+0$

$\Rightarrow b=c$

Now, $(1,2)$ is midpoint of $(a,0)$ and $(0,b)$

ie. $2=\frac{0+b}{2}$

$\Rightarrow \frac{c}{2}=2$

$\Rightarrow c=4$

and

$1=\frac{a+0}{2}$

$\Rightarrow 1=\frac{-c}{2m}$

$\Rightarrow m=-\frac{c}{2}$

$\Rightarrow m=-2$

$\therefore$ The line is given by $y+2x=4$