Let the point on x-axis be P(x, 0) and the given points be A(7, 6) and B(– 3, 4).
∴ AP = BP
⇒ \(\sqrt{(7-x)^2 +(6-0)^2}\)
= \(\sqrt{(-3-x)^2+(4-0)^2}\)
⇒ (7 − x)2 + 36 = (3 + x)2 + 16
⇒ 49 − 14x + x2 + 36 = 9 + 6x + x2 + 16
⇒ 20x = 85 − 25 = 60
⇒ x = 3
∴ The required point is P(3, 0).