Question

The point which is equidistant from the points $(a,0,0),(0,b,0),(0,0,c)$ and $(0,0,0)$ is:

• A. $(a,b,c)$
• B. $(\sqrt{a},\sqrt{b},\sqrt{c})$
• C. $(2a,2b,2c)$
• D. $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$

Answer 1

The correct option is D $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$

Let the point $(x,y,z)$ be the equidistant from $(a,0,0),(0,b,0),(0,0,c)$ and $(0,0,0)$.

$\Rightarrow (x-a{)}^2+(y-0{)}^2+(z-0{)}^2=(x-0{)}^2+(y-b{)}^2+(z-0{)}^2$
$=(x-0{)}^2+(y-0{)}^2+(z-c{)}^2=(x-0{)}^2+(y-0{)}^2+(z-0{)}^2$

Solving above equations, we get $x=\frac{a}{2},y=\frac{b}{2},z=\frac{c}{2}$