Question

5.
The perpendicular bisector of the line segment joining the points
A(a,0) and B(-a,0) cuts the x - axis at the point ...​

Answer 1

At the point (0,0) i.e. origin.

Step-by-step explanation:

The points A(a,0) and B(-a,0) both lie on the x-axis for any real constant value of a.

So, the line joining points A and B will be the x-axis itself.

Now, perpendicular lines to the x-axis are either the y-axis or parallel to the y-axis.

Now, the midpoint of the line segment AB will be $(\frac{a - a}{2},\frac{0 + 0}{2}) = (0,0)$ i.e. the origin.

Therefore, the perpendicular bisector of the line segment joining points A and B is the y-axis, and therefore, it will cut the x-axis at the point (0,0) i.e. origin. (Answer)