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) $

Given:

The line segment joining the points \( A(-2,-5) \) and \( B(2,5) \).

To do:

We have to find the point which lies on the perpendicular bisector of the line segment joining the points \( A(-2,-5) \) and \( B(2,5) \).

Solution:

We know that,

The perpendicular bisector of a line segment divides the line segment into two equal parts.

The perpendicular bisector of the line segment passes through the mid-point of the line segment.

The mid-point of the line segment joining the points $A (-2, -5)$ and $B(2, 5)$ is,

Using mid-point formula, we have

$( x,\ y)=( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})$

$=( \frac{-2+2}{2}, \frac{-5+5}{2})$

$=( \frac{0}{2}, \frac{0}{2})$

$=( 0, 0)$

The point which lies on the perpendicular bisector of the line segment joining the points \( A(-2,-5) \) and \( B(2,5) \) is $(0, 0)$.