what do you mean by external and internal division - Maths - Introduction to Three Dimensional Geometry

Question

what do you mean by external and internal division?

ramandeep.singh · Accepted Answer

Internal division: Consider the point $P (x_{P}, y_{P})$ ) that lies on the line segment AB joining the points $A (x_{A}, y_{A})$ and $B (x_{B}, y_{B})$ Point P divides AB internally in the ratio $k_{1} : k_{2}$ , and the coordinates of point P are given by:-

$P (x_{P}, y_{P}) = (\frac{k_{1} x_{B} + k_{2} x_{A}}{k_{1} + k_{2}}, \frac{k_{1} y_{B} + k_{2} y_{A}}{k_{1} + k_{2}})$ External division: Consider the point $P (x_{P}, y_{P})$ ) that lies outside line segment AB joining the points $A (x_{A}, y_{A})$ and $B (x_{B}, y_{B})$ Point P divides AB externally in the ratio $k_{1} : k_{2}$ , and the coordinates of point P are given by:-

$P (x_{P}, y_{P}) = (\frac{k_{1} x_{B} - k_{2} x_{A}}{k_{1} - k_{2}}, \frac{k_{1} y_{B} - k_{2} y_{A}}{k_{1} - k_{2}})$