The point on the x-axis which is equidistant


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

(a) (0, 2)                        

(b) (2, 0)                         

(c) (3, 0)                         

(d) (0, 3)                                                                                                                  [CBSE 2013]


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).

∴ PA = PB

$\Rightarrow \mathrm{PA}^{2}=\mathrm{PB}^{2}$

$\Rightarrow[x-(-1)]^{2}+(0-0)^{2}=(x-5)^{2}+(0-0)^{2}$ (Using distance formula)


$\Rightarrow x^{2}+2 x+1=x^{2}-10 x+25$

$\Rightarrow 12 x=24$


$\Rightarrow x=2$

Thus, the required point is (2, 0).

Hence, the correct answer is option B.


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