Question

Let $A(6,-5)$ and $B(-6,1)$ be the two vertices of the triangle $ABC$, if the locus of centroid of $△ABC$ is $2x+5y=1$, then the locus of vertex $C$ is

• A. $5x-2y=17$
• B. $2x+5y=23$
• C. $2x-5y=21$
• D. $5x+2y=19$

Answer 1

The correct option is B $2x+5y=23$

Let the coordinates of $C$ be $(a,b)$, then the coordinates of centroid are $(\frac{a+6-6}{3},\frac{b-5+1}{3})=(\frac{a}{3},\frac{b-4}{3})$
Since, the centroid has the locus $2x+5y=1$, then
$2\left(\frac{a}{3}\right)+5\left(\frac{b-4}{3}\right)=1$
$2a+5(b-4)=3$
$2a+5b=23$
Therefore the locus of vertex $C(a,b)$ is $2x+5y=23$.