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  • In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

Q : 14     In what ratio, the line joining  \small (-1,1)  and  \small (5,7)  is divided by the line  x+y=4 ?

Answers (1)

best_answer

Equation of line joining  \small (-1,1)  and  \small (5,7) is
(y-1)= \frac{7-1}{5+1}(x+1)
\Rightarrow (y-1)= \frac{6}{6}(x+1)
\Rightarrow (y-1)= 1(x+1)
\Rightarrow x-y+2=0
Now, point of intersection of lines x+y=4  and x-y+2=0    is   (1,3)
Now, let's suppose point (1,3)divides the line  segment   joining  \small (-1,1)  and  \small (5,7)   in  1:k
Then,
(1,3)= \left ( \frac{k(-1)+1(5)}{k+1},\frac{k(1)+1(7)}{k+1} \right )
1=\frac{-k+5}{k+1} \ \ and \ \ 3 = \frac{k+7}{k+1}
\Rightarrow k =2
Therefore, the line joining  \small (-1,1)  and  \small (5,7)  is divided by the line  x+y=4  in ratio 1:2

Posted by

Gautam harsolia

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