Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Division Formula

(i) Internal Division:

If  A-P-B , the  P is said to be divide the line segment  AB internally in the ratio  m:n , where coordinates of   A , B, and  P are (x_1,y_1), (x_2,y_2) and (x,y) respectively, and   \dfrac{PA}{PB}=\dfrac{m}{n} , then  x=\dfrac{mx_2+nx_1}{m+n}, \quad y=\dfrac{my_2+ny_1}{m+n}

Hence,  PA+PB=AB

(ii) External Division:

If  P-A-B or A-B-P , then  P is said to be divide the line segment  \overline{AB} externally into the segments  \overline{PA} and  \overline{PB} .

The ratio of external division being given by either  PA: PB or  PB : PA  .

Hence |PA-PB|=AB

Case (1)

Hence  PB-PA=AB

Case (2)

Hence  PA-PB =AB

Formula:

If  P (x,y) divides  \overline{AB} , the line segment joining  A(x_1,y_1) and  B (x_2, y_2) externally where  \dfrac{PA}{PB}=\dfrac{m}{n} , then  x=\dfrac{mx_2-nx_1}{m-n}, \quad y=\dfrac{my_2-ny_1}{m-n}

 

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