Question

The equation of the straight line which passes through the intersection of the lines $x+2y=5$ and $3x+7y=17$ and is perpendicular to the line $3x+4y=14$ is

• A. $4x-3y+2=0$
• B. $4x+3y+2=0$
• C. $4x-3y-2=0$
• D. $4x-3y+4=0$

Answer 1

The correct option is A $4x-3y+2=0$

Intersection of the lines $x+2y=5$ and $3x+7y=17$ is $(1,2)$
Now equation of line perpendicular to the line $3x+4y=14$ is
$4x-3y=d$
$\because$ it passes through $(1,2)$
$\therefore d=-2$
Hence equation of the line is $4x-3y+2=0$