Question

Equation of the line perpendicular to the line $6x+2y+7=0$ and which dIvides the line segment joining the points $(5,-3)$ and $(0,2)$ internally in the ratio $7:4$ is

• A. $11x-33y-14=0$
• B. $11x-33y+14=0$
• C. $33x-11y-14=0$
• D. $33x-11y+14=0$

Answer 1

The correct option is A $11x-33y-14=0$

The point which divides the join of $(5,-3)$ and $(0,2)$ in the ratio $7:4$ is

$(\frac{7\left(0\right)+4\left(5\right)}{7+4},\frac{7\left(2\right)+4(-3)}{7+4})=(\frac{20}{11},\frac{2}{11})$

The equation of the line passing through $(\frac{20}{11},\frac{2}{11})$ and perpendicular to $6x+2y+7=0$ is

$2(x-\frac{20}{11})-6(y-\frac{2}{11})=0\Rightarrow (11x-20)-3(11y-2)=0\Rightarrow 11x-33y-14=0$