Question

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

Options

• (0, 0)

• (0, 2)

• (2, 0)

• (–2, 0)

Answer 1

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).

Explanation:

We know that, the perpendicular bisector of the any line segment divides the segment into two equal parts i.e., the perpendicular bisector of the line segment always passes through the mid-point of the line segment.

Mid-point of the line segment joining the points A(–2, –5) and B(2, 5)

= `((-2 + 2)/2, (-5 + 5)/2)`  ...`["Since, mid-point of any line segment which passes through the points"  (x_1, y_1)  "and"  (x_2, y_2) = ((x_1 + x_2)/2, (y_1 + y_2)/2)]`

= (0, 0)  

Hence, (0, 0) is the required point lies on the perpendicular bisector of the lines segment.