Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.
(6a+2a+1,8a+4a+1)
The point, say P(x, y), divides the line AB into the ratio a : 1. The formula for the point that divides a line in the ratio m : n is,
((n×x1+m×x2)m+n,n×y1+m×y2m+n)
Where (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line segment AB
Applying the formula, we get ((1×2+a×6)a+1,1×4+a×8a+1)=(6a+2a+1,8a+4a+1)