Question

$A(2,-5)$ and $B(-7,6)$ are two vertices of a triangle. Find the equation of the locus of the third vertex $C$, if the centroid of the triangle lies on the locus $3x-4y+11=0$

Answer 1

$A(2,-5),B(-7,6)$ and C be $(h,k)$

Now centroid of $△ABC=(\frac{2-7+h}{3},\frac{-5+6+k}{3})$

Given that centroid lies on $3x-4y+11=0$

=>$3(5+h)-4(1+k)+33=0$

=>$3h-4k+44=0$

locus of Vertex C=$3x-4y+44=0$