Question

Let $PS$ be the median of a triangle with vertices $P(2,2),$ $Q(6,-1)$ and $R(7,3).$ The equation of the 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 $2x+9y+7=0$

Median through $P$ bisects $QR$.
Hence, coordinates of $S$ are $(\frac{6+7}{2},\frac{-1+3}{2})=(\frac{13}{2},1)$
Slope of $PS$ is $\frac{1-2}{13/2-2}=\frac{-2}{9}$
Equation of line passing through $(1,-1)$ and parallel to $PS$ is $y+1=\frac{-2}{9}(x-1)$
$\Rightarrow 2x+9y+7=0$