Question

Let PS be the median of the triangle with vertices $P(2,2),Q(6,-1)$ and $R(7,3).$ The equation of a line parallel to PS passing through (-1,1) 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 the mid-point of $Q$ and $R$
$\therefore S=\frac{7+6}{2},\frac{3-1}{2}=\frac{13}{2},1$
Now, slope of $PS=m=\frac{2-1}{2-\frac{13}{2}}=-\frac{2}{9}$
Now, equation of the line passing through $(1,-1)$ and parallel to $PS$ is
$y+1=\frac{2}{9}(x-1)\Rightarrow 2x+9y+7=0$