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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-opti

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

\mathrm{y-3=\frac{1-3}{4-2}(x-2)}
or \mathrm{x+y= 5 \quad \ldots(i)}
Let the line joining (1,2) and (4,3) is divided in the ratio \mathrm{K: 1}.
The point where it is divided is \mathrm{\left(\frac{4 \mathrm{~K}+1}{\mathrm{~K}+1}, \frac{3 \mathrm{~K}+2}{\mathrm{~K}+1}\right)}

But the point is lying on (i)
\mathrm{\frac{4 \mathrm{~K}+1}{\mathrm{~K}+1}+\frac{3 \mathrm{~K}+2}{\mathrm{~K}+1}=5}

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

\mathrm{\therefore}  Required ratio is \mathrm{1: 1}

Hence (C) is the correct answer.

 

Posted by

Ritika Kankaria

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