If the point (x1+t(x2−x1),y1+t(y2−y1)) divides the join of (x1,y1) and (x2,y2) internally, then

(x1+t(x2−x1),y1+t(y2−y1))≡(x1(1−t)+tx2,y1(1−t)+ty2) is the point which divides the join of (x1,y1)  and  (x2,y2) in the ration t:(1−t),which is positive if 0