Question

Let $A(-3,2)$ and $B(-2,1)$ be the vertices of a triangle ABC. If the centroid of triangle ABC lies on the line $3x+4y+2=0$ which doesn't pass through any vertex, then the locus of vertex C is?

• A. $4x+3y+5=0$
• B. $3x+4y+3=0$
• C. $4x+3y+3=0$
• D. $3x+4y+5=0$

Answer 1

Answer: (B)

$3x+4y+3=0$

Let the third vertex be $(h,k)$

Given $A(-3,2)$ and $(-2,1)$

Centroid of the triangle is $(\frac{-3-2+h}{3},\frac{2+1+k}{3})=(\frac{h-5}{3},\frac{k+3}{3})$

Given centroid lies on the line $3x+4y+2=0$

$⟹\frac{3(h-5)}{3}+\frac{4(k+3)}{3}+2=0$

$⟹3(h-5)+4(k+3)+6=0$

$⟹3h+4k+3=0$

The locus of vertex $C$ is $3x+4y+3=0$