A) \[(0,0)\]
B) \[(0,2)\]
C) \[(2,0)\]
D) \[(-2,0)\]
Correct Answer: A
Solution :
| [a] We know that, the perpendicular bisector of any line segment divides the line segment into two equal parts i.e., the perpendicular bisector of the line segment always passes through the mid-point of the line segment. |
| Since, mid-point of any line segment which passes through the points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})=\,\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\] |
| \[\therefore \]Mid-point of the line segment joining the |
| points |
| \[A(-2-5)\]and \[B(2,5)=\left( \frac{-2+2}{2},\frac{-5+5}{2} \right)=(0,0)\] |
| Hence, \[(0,0)\] is the required point which lies on the perpendicular bisector of the line segment AB. |
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