The ___________ is used to find the coordinates of the point that divides a line segment (externally or internally) into some ratio. 

• When any point divides a line segment externally or internally in some ratio, then the section formula is used to find the coordinates of that point.
• It is the best method used to find the coordinates of the point dividing the line segment in some ratio.

The section formula can be used to find the coordinates of a point that lies on a line segment connecting two given points, say A(x₁,y₁) and B(x₂,y₂), and divides it in the ratio m:n. The formula for finding the coordinates of the point P(x, y) that divides the line segment AB  (externally or internally) in the ratio m:n is given by:

For internally,

section formula:  $\mathrm{x}=\frac{{\mathrm{mx}}_2+{\mathrm{nx}}_1}{\mathrm{m}+\mathrm{n}} \mathrm{and} \mathrm{y}=\frac{{\mathrm{my}}_2+{\mathrm{ny}}_1}{\mathrm{m}+\mathrm{n}}$

For externally,

section formula:  $\mathrm{x}=\frac{{\mathrm{mx}}_2-{\mathrm{nx}}_1}{\mathrm{m}-\mathrm{n}} \mathrm{and} \mathrm{y}=\frac{{\mathrm{my}}_2-{\mathrm{ny}}_1}{\mathrm{m}-\mathrm{n}}$