A) \[x+y-3=0\]
B) \[2x-y=9\]
C) \[x+2y=2\]
D) \[2x+y=7\]
Correct Answer: C
Solution :
Let the points be A (3, - 4) and B (5, 2) and mid point of AB = (4, -1). It is given that the bisecting line intercept the co-ordinate axes in the ratio \[2:1\]. \[\therefore \] Point of co-ordinate axes are (2k, 0) and (0,k). The equation of line passing through the above point is \[y-0=\frac{k-0}{0-2k}\,(x-2k)\] or \[y=-\frac{1}{2}\,(x-2k)\] ... (i) Since, it is passing through the mid point of AB i.e. (4, -1) \[\Rightarrow \] \[-1=-\frac{1}{2}\,(4-2k)\] \[\Rightarrow \] \[2=4-2k\,\,\,\Rightarrow \,\,\,k=1\] Putting the value of k in equation (i), we get \[y=-\frac{1}{2}\,(x-2)\] \[\Rightarrow \] \[x+2y=2\]
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