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

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

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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).

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