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\[x = \dfrac{{m{x_2} + n{x_1}}}{{m + n}}\]

\[y = \dfrac{{x{y_2} + n{y_1}}}{{m + n}}\]

Where \[({x_1}{y_1})\] and \[({x_2},{y_2})\]6- coordinates of points given.

Let ratio is \[k:1\]

Let point given are \[A(15,5)\] and \[B(9,20)\]

\[{x_1} = 15,{y_1} = 5\] and \[{x_2} = 9,{y_2} = 20\] and \[m:n\] is \[k:1\]

\[x = \dfrac{{k \times 9 + 1 \times 15}}{{K + 1}},\,y = \dfrac{{k \times 20 + 1 \times 5}}{{K + 1}}\]

\[x = \dfrac{{9k + 15}}{{K + 1}},\,y = \dfrac{{20k + 5}}{{K + 1}}\]

Points \[(11,15)\] divides line joining points \[(15,5)\]and \[(9,20)\]. Here \[x = 11,y = 15\]

So, \[\dfrac{{9k + 15}}{{k + 1}} = 11\]

\[ \Rightarrow 9k + 15 = 11k + 11\]

\[ \Rightarrow 9k - 11k = 11 - 15\]

\[ \Rightarrow - 2k = - 4\]

\[ \Rightarrow k = 2\]

Ration is \[2:1\]

here in this question we can also points \[y = 15\]equals to \[\dfrac{{20k + 15}}{{k + 1}}\] and get \[k = 2\]