The correct option is C 1
Given lines may written as y+3x=0,2y−x=0 and x+y=k
Solving these three we get the vertices of required triangle, which are
(0,0),(2k3,k3) and (−k2,3k2)
Thus centroid of the triangle is (k18,11k18)
Comparing with the given value we get, ⇒k=1