Find the point on x-axis which is equidistant from points A(-1, 0…

Question

Find the point on x-axis which is equidistant from points A(-1, 0) and B(5, 0).

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Answer

Let P(x, 0) be the point on x-axis. Then
$AP = BP$
$\Rightarrow AP^2 = BP^2$
$\Rightarrow (x + 1)^2 + (0 - 0)^2 = (x - 5)^2 + (0 - 0)^2$
$\Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25$
$\Rightarrow 12x = 24$
$\Rightarrow x = 2$
Hence, x = 2.

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