Question

Question 10
The point which lies on the perpendicular bisector of a line segment joining points A(-2, -5) and B(2,5) is
(A) (0, 0)
(B) (0, 2)
(C) (2, 0)
(D) (–2, 0)

Answer 1

We know that, the perpendicular bisector of a line segment divides the line segment into two equal parts i.e., the perpendicular bisector of a line segment always passes through mid-point of the line segment.
$\therefore$ Mid-point of the line segment joining points A(-2,-5) and B(2,5)
$=(\frac{-2+2}{2},\frac{-5+5}{2})=(0,0)$
[$\because$ Mid-point of any line segment which passes through points
$(x_1,y_1)$ and $(x_2,y_2)$ is $[\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}]$
Hence, (0,0) is the required point that lies on the perpendicular bisector of the line segment.