Let P be the point that divides the line segment AB in the ration AP:PB=m:n.

If O is the origin show that

OP=(n/m+n)OA + (m/m+n)OB

Dear stuednt,

C divides AB internally.

Let A (x₁, y₁) and B (x₂, y₂) be the two points joined by line segment AB. Let C (x, y) be the point on the line segment such that 

(In this case, AC and CB are real in the same direction on the line AB.)

Draw AP, CR and BQ perpendicular to x-axis.

AM perpendicular to CR and CM perpendicular to BQ.

AM = PR = x-x₁

CN = RQ = x₂-x

CM = y-y₁

BN = y₂-y

From the similar triangles, CAM and BCN, we have