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I already know how to get the section formula with the help of similarity of triangles concept, what i want to know know is whether i can get the same formula using the concept of distance between two coordinate points, i.e. for A(x1,y1) and B(x2,y2) distance AB = now suppose that a point C divides AB in the ratio m : n, then using the distance formula and using can we get coordinates of C as .


I already know how to get the section formula with the help of similarity of triangles 


concept, what i want to know know is whether i can get the same formula using the concept of distance between two coordinate points, 


i.e. for A(x1,y1) and  B(x2,y2) distance AB =     



 d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\,



now suppose that a point C divides AB in the ratio m : n, then using the distance formula 


   d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\, and using


  


can we get coordinates of C as




.

Grade:12

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
420 Points
13 years ago

Dear Neel

You have to also apply the slope of AC= slope of CB

it will give you y-y1/x-x1 = y-y2/x-x2

as you are using only distance relation that is not sufficient.line ac and cb can be inclined also and can

 satisfy ac/cb=m/n

 

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

 

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