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I know that the section formula can be derived by using the similarity of triangles concept.


But can it also be be derived using the distance between two points concept, i.e., for line AB with point p dividing it in the ratio m : n; here A = (x1,y1), B = (x2,y2) and p = (x,y).


 


(distance of AP) / (distance of PB) = m/n


 


I tried doing it but got ended up getting a very scary looking expression.


Any help in this regard will be really appreciated.


-Neel.


 

6 years ago

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Answers : (2)

										

Dear student,


You are on the right track and this is the way of solving section formula....














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6 years ago
										

section formula


 


if a company wants to insert a tower between two points in a way such that building of  darshanam vatika is 5 times nearer to tower than the building of gordhan park.


 


darshanam vatika(34km,28km);gordan park(83km,56km)


 


position of tower=[5*34+83]/6 , 5*28+56/6]


                       = [253/6,196/6]


                       = [42.16km,32.66km]


the distance between dv and gp is divided in such a way that the tower is five times as close to dv than gp.Thuscoordinates of dv is taken five times than coordinates of gp.


you can check this:


difference of tower from dv(x coordinate)=42.16-34=8.16


difference of tower from gp(x coordinate)=42.16-83=-40.84km 0r distance=40.84km


therefore;40.84/8.16=5


 


 


 


 

4 years ago

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