Question

The equation of the straight line which bisects the intercepts between the axes of the lines $x+y=2$ and $2x+3y=6$ is

• A. $2x=3$
• B. $y=1$
• C. $2y=3$
• D. $x=1$

Answer 1

The correct option is B $y=1$

Given lines are lines $x+y=2$ and $2x+3y=6$
$x+y=2$ cuts the $x$ and $y$ axis at $(2,0),(0,2)\Rightarrow \text{Midpoint}=(1,1)$ and $2x+3y=6$ cuts the $x$ and $y$ axis at $(3,0),(0,2)\Rightarrow \text{Midpoint}=(\frac{3}{2},1)$
Slope of line joining midpoints $=0$
Hence, the equation of a straight line which bisects the intercepts made by the axes on the lines $x+y=2$ and $2x+3y=6$ is given by $y=1$