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