B(4,7)   and  C(6,1)   are two vertices of a ΔABC . If vertex A moves on the line 9x+7y=28,  then the locus of the centroid ΔABC  is a line parallel to

Let the vertex A be (a,b)  .   ∴9a+7b=28   …….(1) If the coordinates of the centroid are (x,y),  then    3x=a+4+6  and  3y=b+7+1 ∴   a=3x−10   and  b=3y−8 Putting these values in (1) , we get 9(3x−10)+7(3y−8)=28 (i.e.)3(9x+7y)−174=0⇒9x+7y−58=0  which is a parallel to 9x+7y=28.