Question

The point which lies on the perpendicular bisector of the line segment joining the points A(−2, −5) and B(2, 5) is

(a) (0, 0)
(b) (0, 2)
(c) (2, 0)
(d) (−2, 0)

Answer 1

(a) (0, 0)
The point which lies on the perpendicular bisector of AB is the midpoint of AB.
The given points are $A\left(-2,-5\right)\text{and}B\left(2,5\right)$.
Here, $\left(x_1=-2,y_1=-5\right)\text{and}\left(x_2=2,y_2=5\right)$
$$\begin{gathered} \text{Midpoint of}AB=\left(\frac{-2+2}{2},\frac{-5+5}{2}\right) \\ \text{i.e.}\left(0,0\right) \end{gathered}$$
Hence, the required point is (0,0).