Let mathrm{C} be centroid of triangle with vertices (3,-1),(1,3) and (2,4) . Let P be point of inter

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9.Straight Line

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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 $3 \mathrm{x}-\mathrm{y}+1=0 .$ Then the line passing through the points $\mathrm{C}$ and $\mathrm{P}$ also passes through the point

A

$(7, 6)$

B

$(-9, -6)$

C

$(-9, -7)$

D

$(9, 7)$

(JEE MAIN-2020)

Solution

Centroid of $\Delta=(2,2)$

line passing through intersection of $x+3 y-1=0$ and

$3 x-y+1=0,$ be given by

$(x+3 y-1)+\lambda(3 x-y+1)=0$

$\because$ It passes through $(2,2)$

$\Rightarrow \quad 7+5 \lambda=0 \Rightarrow \lambda=-\frac{7}{5}$

$\therefore \quad$ Required line is $8 x-11 y+6=0$

$(-9,-6)$ satisfies this equation

Standard 11

Mathematics

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