The points (k,2−2k),(−k+1,2k)  and  (−4−k,6−2k)  are collinear for

The given points are collinear, ifArea of Δ=0⇒    k2−2k1−k+12k1−4−k6−2k1=0Applying R2→R2−R1,R3→R3−R1⇒    −2k+14k−2−4−2k4=0⇒        (1−2k)(k+1)=0⇒  k=−1  or  k=12 ,  neglecting 12  as when k=12 , points are same.