Section formula is basically used in coordinate geometry where coordinate geometry is defined as a system or part of geometry where ordered pairs of numbers are used to describe position of points on any plane. A plane is a flat surface which consists of two axes that is x - y plane where x and y- axis are considered. y - z plane is a plane where y and z axes are considered and x - z plane is a plane where x and z axes are considered. Section formula is categorized in two forms that are internally divided and externally divided.
Let us consider a line segment having two end points as (x, y) and (u, v). Now consider a point say 'T' which divides line segment into ratio of 'm' and 'n'.
Section Formula, when point 'T' divides line segment internally is given by:
[(mu + nx)/m+n, (mv + ny)/ m+n],
And the section formula when 'T' divides line segment externally is given as:
[(mu – nx) / m - n , (mv – ny) / m - n].
In coordinate geometry using section formula we can determine the distance between two points. It can be used to determine midpoints, equation of line segment and slope of line segment. It is used to determine whether lines are perpendicular or parallel. It can also be used to determine area and perimeter of different types of polygon. It is also used to define equations of different types of curves like circles, ellipses and more.
Suppose a line segment AB whose end points are A(x, y) and B(u, v). then the midpoint of this line segment is given by [(x + u) / 2 , (y + v) / 2].