Question

Let PS be the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$ and $R(7,3)$. The equation of line passing through $(1,-1)$ and parallel to PS is :

• A. $2x-9y-7=0$
• B. $2x-9y-11=0$
• C. $2x+9y-11=0$
• D. $2x+9y+7=0$

Answer 1

The correct option is D $2x+9y+7=0$

Since $S$ is mid point of $Q$ and $R$

$\therefore S=(\frac{7+6}{2},\frac{3-1}{2})=(\frac{13}{2},1)$

Slope of $PS=m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{2-\frac{13}{2}}=\frac{-2}{9}$

Equation of the line passing through $(1,-1)$ and parllel to $PS$ is

$y-(-1)=\frac{-2}{9}(x-1)$

$y+1=\frac{-2x+2}{9}$

$\Rightarrow 9y+9+2x-2=0$

$\Rightarrow 2x+9y+7=0$