Let C be the centroid of the triangle with vertices ( 3 , - 1 ) , ( 1 , 3 ) and ( 2 , 4 ) . Let P be the point of intersection of the lines x + 3 y - 1 = 0 and 3 x - y + 1 = 0 . Then the line passing through the points C and P also passes through the point

Step-by-step solution

The centroid of a triangle having vertices x 1 , y 1 ,   x 2 , y 2 and x 3 , y 3 is x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 . The centroid of the triangle having vertices ( 3 , - 1 ) ,   ( 1 , 3 ) and ( 2 , 4 ) is C 3 + 1 + 2 3 , - 1 + 3 + 4 3 = ( 2 , 2 ) . The equation of a line passing through the point on intersection of lines L 1 = 0 and L 2 = 0 is L 1 + λ L 2 = 0 . Thus, the equation of line which passes through point of intersection P of lines x + 3   y - 1 = 0 and 3   x - y + 1 = 0 is