- Home
- Standard 11
- Mathematics
9.Straight Line
hard
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
