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Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

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Let (a, 0) be the point on the x axis that is equidistant from the points (7, 6) and (3, 4). On squaring both sides, we obtain a2 – 14a + 85 = a2 – 6a + 25 ⇒ –14a + 6a = 25 – 85 ⇒ –8a = –60 Thus, the required point on the x-axis is.
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Let (a, 0) be the point on the x axis that is equidistant from the points (7, 6) and (3, 4).

On squaring both sides, we obtain

a2 – 14a + 85 = a2 – 6a + 25

⇒ –14a + 6a = 25 – 85

⇒ –8a = –60

Thus, the required point on the x-axis is.

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