Let C be the centroid of the triangle


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:

  1. (1) $(-9,-6)$

  2. (2) $(9,7)$

  3. (3) $(7,6)$

  4. (4) $(-9,-7)$

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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