Question

Find the coordinates of the point on the $x$-axis that is equidistant from $P(4,3,1)$ and $Q(-2,-6,-2)$.

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

Answer 1

The correct option is B $(-\frac{3}{2},0,0)$

Let $R(x,0,0)$ be the point on $x$-axis which is equidistant from $P(4,3,1)$ and $Q(-2,-6,-2)$

$\Rightarrow {(x-4)}^2+{(-3)}^2+{(-1)}^2={(x+2)}^2+6^2+2^2$ gives $-12x=18$

So $x=-1.5$

Hence, $R\equiv (-\frac{3}{2},0,0)$