Find the point on x-axis which is equidistant from the points (2,-5) and (-2,9)

Let the point on x-axis is P(x, 0), which is equidistant from the points (2,-5) and (-2, 9)

We know the distance formula between two points is,

       …… (1)

So, distance between the point P(x, 0) and A (2,-5) is,

And the distance between the point P(x, 0) and B (-2, 9) is,

Since (x, 0) is equidistant from the other two point.

So,

Squaring on both sides, we have

Hence required point is (-7, 0).