Let $\mathrm{C}$ be the centroid of the triangle with vertices $(3,-1)$, $(1,3)$ and $(2,4)$. Let $P$ be the point of intersection of the lines $x+3 y-1=0$ and $3 x-y+1=0$. Then the line passing through the points $C$ and $P$ also passes through the point:
Correct Option: 1
Coordinates of centroides
$C=\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$
$=\left(\frac{3+1+2}{3}, \frac{-1+3+4}{3}\right)=(2,2)$
The given equation of lines are
$x+3 y-1=0$ $\ldots$..(i)
$3 x-y+1=0$...(ii)
Then, from (i) and (ii)
point of intersection $P\left(-\frac{1}{5}, \frac{2}{5}\right)$
equation of line $D P$
$8 x-11 y+6=0$
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