Given vertices (x1,y1),(x2,y2),(x3,y3)(x_1,y_1), (x_2,y_2), (x_3,y_3)(x1,y1),(x2,y2),(x3,y3): area =12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣= \tfrac{1}{2}\big|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)\big|=21x1(y2−y3)+x2(y3−y1)+x3(y1−y2). If this is 000, the three points are collinear.