Question

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

Options

• (0, 2)   

• (2, 0)

• (3, 0)     

• (0, 3)

Answer 1

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).
∴ 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)

\[\Rightarrow \left( x + 1 \right)^2 = \left( x - 5 \right)^2 \]
\[ \Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25\]
\[ \Rightarrow 12x = 24\]
\[ \Rightarrow x = 2\]

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