If the point  x1+tx2−x1,y1+ty2−y1)divides the join of x1,y1 and x2,y2 internally, then

The co-ordinates of the point of division arex1+tx2−x1,y1+ty2−y1=(1−t)x1+tx2(1−t)+t,(1−t)y1+ty2(1−t)+tClearly, these are the coordinates of the point dividing the jo of x1,y1 and x2,y2 in the ratio t:(1−t). For the internal division, we must havet>0  and  1−t>0⇒0