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
⇒ x2 – 14x + 49 + 36 = x2 + 6x + 9 + 16
⇒ – 20x = – 60
⇒ x = 3
Therefore, the point on the x - axis is (3, 0).
