The point on the x-axis which is equidistant from points (–1, 0) and (5, 0) is ______.

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KollegeApply · Accepted Answer

The point on the x-axis which is equidistant from points (–1, 0) and (5, 0) is (2, 0). Explanation: Let A(−1, 0) and B(5, 0) be the given points. Suppose the required point on the x-axis be P(x, 0). It is given that P(x, 0) is equidistant from A(−1, 0) and B(5, 0). $\therefore$ PA = PB $\Rightarrow$ PA2 = PB2 \Rightarrow \left[ x - \left( - 1 \right) \right]^2 + \left( 0 - 0 \right)^2 = \left( x - 5 \right)^2 + \left( 0 - 0 \right)^2 (Using distance formula) \Rightarrow \left( x + 1 \right)^2 = \left( x - 5 \right)^2 \Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25 \Rightarrow 12x = 24 \Rightarrow x = 2 Thus, the required point is (2, 0).

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