A) 3 : 2
B) 3 : 5
C) 2 : 3
D) 2 : 5
Correct Answer: B
Solution :
[b] Let X-axis cut the join of \[A\,(6,\,\,3)\] and \[B\,(-\,2,\,-5)\] in the ratio at \[k:1\] the point P. |
Then, coordinates of P are \[\left( \frac{-\,2k+6}{k+1},\frac{-\,5k+3}{k+1} \right).\] |
But P lies on X-axis. So its ordinate is 0. |
\[\therefore \] \[\frac{-\,5k+3}{k+1}=0\] |
\[\Rightarrow \] \[-\,5k+3=0\]\[\Rightarrow \]\[k=\frac{3}{5}\] |
Hence, required ratio is \[\frac{3}{5}\]i.e. \[3:5.\] |
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