Question

Q.20 find the ratio of a line joining the points (1, 2), (3, 4) intersecting by a point (1/2, 3/4)​

Answer 1

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Q1) Find the ratio of a line joining the points (1,2) ,(3,4) interesting by a point (1/2,3/4)

$\: \: \huge\underline{ \divideontimes \mathtt{ \: answer}}$

$\: \: \: \\ \bullet \underline {\boxed{ \bf{ \: by \: using \: section \: formula}}}$

$\implies\displaystyle\tt{x=\dfrac{mx_1+n_x2}{m+n} \: and \: y=\dfrac{my_1+ny_2}{m+n}}$

$\implies\displaystyle\sf{\dfrac{1}{2}=\dfrac{m\times1+n\times3}{m+n}}$

$\implies\displaystyle\sf{m+n=2(m+3n)}$

$\implies\displaystyle\sf{m+n=2m+3n}$

$\implies\displaystyle\sf{m+n-2m-3n=0}$

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

$\implies\displaystyle\sf{m+2n=0 .........(1)}$

$\implies\displaystyle\tt{y=\dfrac{my_1+ny_2}{m+n}}$

$\implies\displaystyle\sf{\dfrac{3}{4}=\dfrac{m\times2+n\times4}{m+n}}$

$\implies\displaystyle\sf{3(m+n)=4(2m+4n)}$

$\implies\displaystyle\sf{3m+3n=8m+16n}$

$\implies\displaystyle\sf{3m+3n-8m-16n=0}$

$\implies\displaystyle\sf{-5m-13n=0}$

$\implies\displaystyle\sf{5m+13n=0........(2)}$

$\bigstar\displaystyle\bf{Solving\: both \: equations (1) \: and (2)}$

$\sf{m+2n=0 \times 5}$

$\sf{5m+13n=0}$

$\bf{5m+10n=0......(3)}$

$\sf{5m+13n=0}$

$\implies\pink\bf{n=0 \: and\: m=0}$