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 [MP PET 1993]

• 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 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 $x=\frac{a}{2},y=\frac{b}{2}andz=\frac{c}{2}.$