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# Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).

Let the point be (x, 0) on x–axis which is equidistant from (2, –5) and (–2, 9).

Using Distance Formula and according to given conditions we have:

$$\sqrt{(x - 2)^2 + ( 0 - (-5))^2}$$
$$= \sqrt{ (x - (-2))^2 + ( 0 - 9)^2}$$

=>$$\sqrt {x^2 + 4 - 4x + 25}$$
$$= \sqrt {x^2 + 4 + 4x + 81}$$

Squaring both sides, we get
$$\Rightarrow x^2 + 4 - 4x + 25 = x^2 + 4 + 4x + 81$$
$$\Rightarrow-4x + 29 = 4x + 85$$
$$\Rightarrow 8x = -56$$
$$\Rightarrow x = -7$$

Therefore, point on the x–axis which is equidistant from (2, –5) and (–2, 9) is (–7, 0)