Centroid is a point where all the three medians of the triangle intersect. So,the centroid\xa0of triangle can be found by finding the average of the x-coordinate\’s value and the average of the y-coordinate\’s value of all the vertices of the triangleThe vertices of\xa0{tex}\\Delta ABC{/tex}\xa0are (a, b), (b, c) and (c, a)\xa0Therefore Centroid is{tex}\\left( \\frac { x _ { 1 } + x _ { 2 } + x _ { 3 } } { 3 } , \\frac { y _ { 1 } + y _ { 2 } + y _ { 3 } } { 3 } \\right){/tex}or\xa0{tex}\\left( \\frac { a + b + c } { 3 } , \\frac { b + c + a } { 3 } \\right){/tex}But centroid is (0, 0).{tex}\\Rightarrow{/tex}\xa0a + b + c = 0