Question

find the value of k if the points (k, 2k), (-2,6) and (3,1) are collinear​

Answer 1

Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero

The area of the triangle with vertices (x1,y1) ; (x2,y2)  and (x3,y3)  is ∣∣∣∣2x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣∣∣∣

Hence, substituting the points (x1,y1)=(k,2k) ; (x2,y2)=(3k,3k)  and (x3,y3)=(3,1) in the area formula, we get ∣∣∣∣2k(3k−1)+3k(1−2k)+3(2k−3k)∣∣∣∣