question_answer

The equation of the perpendicular bisector of the line segment joining\[A(-2,\text{ }3)\]and\[B(6,-5)\]is

A)  \[x-y=-1\]       

B)         \[x-y=3\]

C)  \[x+y=3\]         

D)         \[x+y=1\]

E)  \[x+y=-1\]

Correct Answer: B

Solution :

The equation of the line passing through the points\[(-2,3)\]and\[(6,-5)\]is \[(y-3)=\frac{-5-3}{6+2}(x+2)\] \[\Rightarrow \]               \[(y-3)=-1(x+2)\] \[\Rightarrow \]               \[y-3=-x-2\] \[\Rightarrow \]               \[y=-x+1\]                                           ?..(i) Now, the slope of perpendicular bisector of this line is\[=\frac{-1}{(-1)}=1\] and the perpendicular bisector passing through the mid point of this line is\[(2,-1)\]. Then, equation of perpendicular bisector is                 \[(y+1)=1(x+2)\] \[\Rightarrow \]               \[y+1=x-2\] \[\Rightarrow \]               \[x-y=3\]