Question

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

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

Answer 1

Answer: (A)

$\left( \frac { a } { 2 } , \frac { b } { 2 } , \frac { c } { 2 } \right)$

Answer 2

Let point be $( x , y , z )$ then $x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$

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

Therefore $x = \frac { a } { 2 } , y = \frac { b } { 2 }$ and $z = \frac { c } { 2 }$ .