A) \[(2,-\,\,3)\]
B) \[(-\,\,1,2)\]
C) \[\left( \frac{3}{2},0 \right)\]
D) \[\left( -\frac{3}{2},0 \right)\]
Correct Answer: D
Solution :
Let the required ratio be k :1 So, the coordinates of the point M of division A\[(1-5),\]and B\[(-\,\,4,5)\] \[\left( \frac{k{{x}_{2}}+1\cdot {{x}_{1}}}{k+1},\frac{k{{y}_{2}}+1\cdot {{y}_{1}}}{k+1} \right)\]i.e.,\[\left( \frac{-\,\,4k+1}{k+1},\frac{5k-5}{k+1} \right)\] But according to question, line segment joining A\[(1,-\,\,5)\]and B\[(-\,\,4,5)\]is divided by the x- axis. So, y-coordinates must be zero. \[\therefore \] \[\frac{5k-5}{k+1}=0\]\[\Rightarrow \]\[5k-5=0\]\[\Rightarrow \]\[5k=5\] \[\Rightarrow \] \[k=1\] So, the required ratio is 1 : 1 and the point of division M is \[\left( \frac{-\,\,4(1)+1}{1+1},\frac{5\,\,(1)-5}{1+1} \right)\] i.e., \[\left( \frac{-\,\,4+1}{2},0 \right)\]or \[\left( -\frac{3}{2},0 \right)\]
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