Question

Let $C$ 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:

• A. ( - 9, -7 )
• B. ( -9 , -6 )
• C. (7, 6)
• D. (9, 7)

Answer 1

Answer: (B)

$Centroid of \Delta = \left(2, 2\right)$
line passing through intersection of
$x + 3y - 1 = 0$ and
$3x - y + 1 = 0$, be given by
$\because$ It passes through $\left(2, 2\right)$
$\Rightarrow 7+5\lambda=0 \Rightarrow \,\lambda=-\frac{7}{5}$
$\therefore $ Required line is $8x - 11y + 6 = 0$
$\because \left(-9, -6\right)$ satisfies this equation.