Let us consider (a, 0) be the point on the x-axis that is equidistant from the point (7, 6) and (3, 4).

So,

\( \sqrt{(7 - a)^2 + (6-0)^2}\)

= \( \sqrt{(3 - a)^2 + (4-0)^2}\)

\( \sqrt{49 + a^2-14a+36 }\)

= \( \sqrt{9 + a^2-6a+16 }\)

\( \sqrt{ a^2-14a+85 }\)

= \( \sqrt{ a^2-6a+25 }\)

Now, let us square on both the sides we get,

a^{2} – 14a + 85 = a^{2} – 6a + 25

-8a = -60

a = \( \dfrac{60}{8}\)

= \( \dfrac{15}{2}\)

The required point is (\( \dfrac{15}{2}\), 0)

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