Question

origin divides the join of points (1,1) and (2,2) externally in the ratio?​

Answer 1

SOLUTION

TO DETERMINE

The ratio origin divides the join of points (1,1) and (2,2) externally

CONCEPT TO BE IMPLEMENTED

Case of externally divide :

$\sf{The \: coordinate \: of \: the \: point \: where \: the \: line }$

$\sf{joining \: the \: points \: (x_1,y_1) \: and \: (x_2,y_2) \: in }$

$\sf{the \: ratio \: \: m :n \: \: is }$

$= \displaystyle \sf{ \bigg( \frac{mx_2-nx_1 \: }{m - n} \: \: , \: \frac{my_2-ny_1 \: }{m - n} \bigg) }$

EVALUATION

Here the given points are (1,1) and (2,2)

Let the required ratio = m : n

So by the given condition

$\displaystyle \sf{ \bigg( \frac{2m-n \: }{m - n} \: \: , \: \frac{2m-n \: }{m - n} \bigg) = ( 0,0)}$

$\displaystyle \sf{ \implies \frac{2m-n \: }{m - n} = 0}$

$\displaystyle \sf{ \implies 2m-n \: = 0}$

$\displaystyle \sf{ \implies 2m = n}$

$\displaystyle \sf{ \implies \frac{m}{n} = \frac{1}{2} }$

$\displaystyle \sf{ \implies \: m : n = 1 :2 }$

Hence the required ratio = 1 : 2

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