Let [A( 2, - 3 )] and [B( -2, 1 )] be vertices of a triangle ABC.

Question

Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2,  1} \right)$$ be vertices of a triangle $ABC$. If the centroid of this triangle moves on the line $2x + 3y = 1$, then the locus of the vertex $C$ is the line :

Accepted Answer

Let the vertex $C$ be $(h,k),$  then the

centroid of $$\Delta ABC$$ is $$\left( {{{2 + (- 2) + h} \over 3},{{ - 3 + 1 + k} \over 3}} \right)$$

or $$\left( {{h \over 3},{{ - 2 + k} \over 3}} \right).$$ It lies on $2x+3y=1$

$$ \Rightarrow {{2h} \over 3} - 2 + k = 1$$

$$ \Rightarrow 2h + 3k = 9$$

$$ \therefore $$ Locus of $C$ is $2x+3y=9$

Solutions · 1