question_answer

A straight line through \[P(1,\,\,2)\] is such that its intercept between the axes is bisected at P. Its equation is:

A) \[x+y=-1\]                          

B) \[x+y=3\]

C) \[x+2y=5\]                         

D) \[2x+y=4\]

Correct Answer: D

Solution :

Since, \[P(1,\,\,2)\] is the midpoint of a line \[AB\], therefore coordinates of \[A\] and \[B\] are \[(2,\,\,0)\] and\[(0,\,\,4)\]. \[\therefore \]Equation of line\[AB\]is                 \[y-0=\frac{4-0}{0-2}(x-2)\] \[\Rightarrow \]               \[y=-2x+4\] \[\Rightarrow \]               \[2x+y=4\]