Question:
The point on x-axis which is equidistant from points A(−1, 0) and B(5, 0) is
(a) $(0,2)$
(b) $(2,0)$
(c) $(3,0)$
(d) $(0,3)$
Solution:
Let P(x, 0) the point on x-axis, then
$A P=B P \Rightarrow A P^{2}=B P^{2}$
$\Rightarrow(x+1)^{2}+(0-0)^{2}=(x-5)^{2}+(0-0)^{2}$
$\Rightarrow x^{2}+2 x+1=x^{2}-10 x+25$
$\Rightarrow 12 x=24 \Rightarrow x=2$
Thus, the required point is (2, 0).
Hence, the correct answer is option (b).
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