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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)
Solution
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).
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