A) 1 : 5
B) 5 : 1
C) 3 : 2
D) 4 : 5
Correct Answer: A
Solution :
Let P \[\left( \frac{3}{4},\frac{5}{12} \right)\] divide AB internally in the ratio m: n. Using the section formula, we get |
\[\left( \frac{3}{4},\frac{5}{12} \right)=\left( \frac{2\,m-\frac{n}{2}}{m+n},\frac{-5\,m+\frac{3}{2}n}{m+n} \right)\] |
On equating, we get |
\[\Rightarrow \]\[\frac{3}{4}=\frac{2\,m-\frac{n}{2}}{m+n}\] |
and\[\frac{5}{12}=\frac{-\,\,5\,m+\frac{3}{2}n}{m+n}\] |
\[\Rightarrow \]\[\frac{3}{4}=\frac{4\,m-n}{2\,\,(m+n)}\] |
and\[\frac{5}{12}=\frac{-\,\,10\,m+3\,\,n}{2\,\,(m+n)}\] |
\[\Rightarrow \] \[\frac{3}{2}=\frac{4\,m-n}{m+n}\]and \[\frac{5}{6}=\frac{-\,\,10\,m+3\,n}{m+n}\] |
\[\Rightarrow \] \[x=1\] |
\[\Rightarrow \] \[5\,m+5\,n=-60\,m+18\,n\] |
\[\Rightarrow \] \[5\,n-5\,m=0\]and \[65\,\,m-13\,\,n=0\] |
\[\Rightarrow \] \[n=m\]and\[13\,\,(5\,m-n)=0\] |
\[\Rightarrow \] \[n=m\]and \[5\,\,m-n=0\] |
\[\because \] \[m=n\] does not satisfy. |
\[\therefore \] \[5\,m-n=0\] |
\[\Rightarrow \] \[5\,\,m=n\] |
\[\Rightarrow \] \[\frac{m}{n}=\frac{1}{5}\] |
You need to login to perform this action.
You will be redirected in
3 sec