(I) Internal Division
If divides the line segment joining
and
internally in ratio
i.e.
then,
Example:
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.
Example:
Let and
be two points.
divides
externally in ratio
then
Midpoint Formula
If be midpoint of
joining
and
then
Example:
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)
Note:
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
(i) Centroid
(ii) Incentre
(iii) Excentre
(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