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  • In which ratio the line joining (2,3) and (4,1) divides the line segment joining (1,2) and (4,3) ?Option: 1  1: 2<div class='qna-o

In which ratio the line joining (2,3) and (4,1) divides the line segment joining (1,2) and (4,3) ?

Option: 1

 1: 2


Option: 2

 2: 1


Option: 3

 1: 1


Option: 4

 2: 3


Answers (1)

best_answer

The equation of line joining (2,3) and (4,1) is

y-3=\frac{1-3}{4-2}(x-2) \text { or } x+y=5 \quad \quad \quad \ldots (i)

Let the line joining (1,2) and (4,3) is divided in the ratio  K: 1.
The point where it is divided is \left(\frac{4 K+1}{K+1}, \frac{3 K+2}{K+1}\right).
But the point is lying on Eq. (i), therefore

\frac{4 K+1}{K+1}+\frac{3 K+2}{K+1}=5
or

4 K+1+3 K+2=5 K+5

or

4 K+1+3 K+2=5 K+5

\therefore Required ratio is 1: 1.

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manish

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