Question

If $C$ be the centroid of the triangle having vertices $(3,-1),(1,3)$ and $(2,4)$. Let $P$ be the point of intersection of the lines $x+3y-1=0$ and $3x-y+1=0$, 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

The correct option is B $(-9,-6)$

Coordinates of $C$ are $(\frac{3+1+2}{3},\frac{-1+3+4}{3})=(2,2)$
Point of intersection of two lines
$x+3y-1=0$ and $3x-y+1=0$
is $P(\frac{-1}{5},\frac{2}{5})$

Equation of line $CP$ is $8x-11y+6=0$
Point $(-9,-6)$ lies on $CP$.