Question

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]

Answer 1

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

⇒ 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)

$$\begin{gathered} \Rightarrow {\left(x+1\right)}^2={\left(x-5\right)}^2 \\ \Rightarrow x^2+2x+1=x^2-10x+25 \\ \Rightarrow 12x=24 \\ \Rightarrow x=2 \end{gathered}$$

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

Hence, the correct answer is option B.