Consider A = (x, 0); B = (2, -5) and C = (- 2, 9).

AB = \(\sqrt{(2-x)^2 + (-5-0)^2}\)

= \(\sqrt{(2-x)^2 + 25}\)

AC = \(\sqrt{(-2-x)^2 + (9-0)^2}\)

= \(\sqrt{(-2-x)^2 + 81}\)

Since both the distance are equal in measure, So AB = AC

\(\sqrt{(2-x)^2 + 25}\) = \(\sqrt{(-2-x)^2 + 81}\)

Simplify the above equation,

Remove square root by taking square both the sides, we get

(2 – x)² + 25 = (-2 – x)² + 81

x² + 4 – 4x + 25 = x² + 4 + 4x + 81

8x = 25 – 81 = -56

x = -7

Therefore, the point is (- 7, 0).