Question

The point on the x-axis equidistant from the points $(4,3,1)$ and $(-2,-6,-2)$ is

• A. $(0,-1,0)$
• B. $(0,1,-6)$
• C. $\left(-\frac{3}{2},0,0\right)$
• D. $\left(-\frac{1}{2},0,0\right)$

Answer 1

Answer: (C)

Let the point on x-axis is $(x,0,0)$
According to the question,
$\sqrt{{(x-4)}^2+{(0-3)}^2+{(0-1)}^2}$
$=\sqrt{{(x+2)}^2+{(0+6)}^2+{(0+2)}^2}$
$\Rightarrow$ $x^2+16-8x+9+1=x^2+4+4x+36+4$
$\Rightarrow$ $12x=26-44=-18$
$\Rightarrow$ $x=\frac{-18}{12}=\frac{-3}{2}$
Hence, required point is $\left(\frac{-3}{2},0,0\right)$ .