Let the point on x - axis be P(x, 0).

**Given:** Point P(x, 0) is equidistant from points A(7, 6) and B(-3, 4)

i.e., distance of P from A = distance of P from B

⇒ \(\sqrt{(x-7)^2+36}\) = \(\sqrt{(x+3)^2+16}\)

**Squaring both sides,**

⇒ (x – 7)^{2} + 36 = (x + 3)^{2} + 16

⇒ x^{2} – 14x + 49 + 36 = x^{2} + 6x + 9 + 16

⇒ – 20x = – 60

⇒ x = 3

**Therefore, the point on the x - axis is (3, 0).**