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  4. If PS is the median of the triangle with vertices P(2,2), Q (6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is

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

JEE MainJEE Main 2014Straight Lines

Solution:

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$S$ is mid-point of $QR$
So $S=\left(\frac{7+6}{2}, \frac{3-1}{2}\right)$
$=\left(\frac{13}{2}, 1\right) $
Slope of $ PS=\frac{2-1}{2-\frac{13}{2}}=-\frac{2}{9}$
Equation of line $\Rightarrow y-(-1)=-\frac{2}{9}(x-1)$
$9 y+9=-2 x+2$
$ \Rightarrow 2 x+9 y+7=0$