Question
Find the point on x-axis which is equidistant from points $A(-1, 0)$ and $B(5, 0)$.
✓
Answer
Let $P(x, 0)$ be the point on x-axis. Then
$AP = BP $
$\Rightarrow AP^2 = BP^2$
$\Rightarrow (x + 1)^2 + (0 - 0)^2 = (x - 5)^2 + (0 - 0)^2$
$\Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25$
$\Rightarrow 12x = 24 $
$\Rightarrow x = 2$
Hence, $x = 2.$
$AP = BP $
$\Rightarrow AP^2 = BP^2$
$\Rightarrow (x + 1)^2 + (0 - 0)^2 = (x - 5)^2 + (0 - 0)^2$
$\Rightarrow x^2 + 2x + 1 = x^2 - 10x + 25$
$\Rightarrow 12x = 24 $
$\Rightarrow x = 2$
Hence, $x = 2.$
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