Question

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

• A. $4x-7y-11=0$
• B. $2x+9y+7=0$
• C. $4x+7y+3=0$
• D. $2x-9y-11=0$

Answer 1

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

$S$ is the mid point of line $QR$


$\therefore$ The coordinates of $S$ are $(\frac{13}{2},1)$
the slope of median $PS$, $m=\frac{1-2}{\frac{13}{2}-2}=-\frac{2}{9}$
The equation of the line passing through point $(1,-1)$ and having slope $-\frac{2}{9}$ is
$y+1=-\frac{2}{9}(x-1)$
$\Rightarrow 2x+9y+7=0$