Question

for what value of k are the points (k,2-2k), (-k+1,2k) and (-4-k,6-2k) are collinear

Answer 1

as the points are collinear the area of the triangle is 0. So put this coordinates in the formula of area of the triangle = 1/2 {x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}

Answer 2

Area should be zero and therefore discriminant should be zero
$\left[\begin{array}{ccc}k&-k=1&-4-k\\2-2k&2k&6-2k\\\end{array}\right]$=o