(I) Internal Division
If divides the line segment joining and internally in ratio i.e.
Let and be two point. divides internally in ratio 2:3 then
(II) External Division
If divides joining and externally in ratio i.e.
It has two cases:
(a) For i.e.
(b) For i.e.
Let and be two points. divides externally in ratio then
If be midpoint of joining and then
Let and be two points in space and be midpoint of , then
Division Formula by ratio
If divides in ratio then coordinates of are given by:
(i) (Internal Division)
(ii) (External Division)
If and are distinct points then the coordinates of any point on except are given by
Formulas to find Coordinates
If , and are vertices of triangle , whose sides are of lengths respectively, then
(a) (to A)
(b) (to B)
(c) (to C)
If are vertices of triangle and and are coordinates of midpoint of respectively,then coordinate of Centroid of