Question

The coordinates of a point which is equidistant from the point $(0,0,0),(a,0,0),(0,b,0)$ and $(0,0,c)$ are given by

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

Answer 1

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

Let $P(x,y,z)$ be the required point.

Then $OP=PA=PB=PC$

Now $OP=PA⟹O{P}^2+P{A}^2⟹x^2+y^2+z^2$

= $(x-a{)}^2+(y-0{)}^2+(z-0{)}^2⟹x=\frac{a}{2}$

Similarily, $OP=PB=y=\frac{b}{2}$ and $OP=PC=z=\frac{c}{2}$

hence the coordinate of the required point are $(\frac{a}{2},\frac{b}{2},\frac{c}{2})$