JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

Let $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3, y_3\right)$ be the vertices of a triangle such that algebraic sum of perpendicular distance from $A, B$ and $C$ to the variable line $a x+b y+c=0$ is always '0'. If $3 a+2 b+c=0$, then find the value of $\sum\limits_{{i=1}}^3\left(x_i+y_i\right)$.