Section Formula

This formula is used to find a point which divides a line given between two points \( (x_1,y_1)\) and \((x_2,y_2)\) in 2D or (\( (x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) in 3D) in a certain ratio. For eg. coordinates for a point that divides the line in l : m ratio are given as:

\(x=\frac{mx_2 + lx_1}{m+l}\)

\(y=\frac{my_2 + ly_1}{m+l}\)

\(z=\frac{mz_2 + lz_1}{m+l}\)

The same formula can be also used to find out points that divide the line externally into any ratio.