Question

The coordinates of the point equidistant from the points (a,0,0),(0,a,0),(0,0,a) and (0,0,0) are

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

Answer 1

The correct option is B $(\frac{a}{2},\frac{a}{2},\frac{a}{2})$

Let the coordinates of the required point be (x,y,z) then
$x^2+y^2+z^2=(x-a{)}^2+y^2+z^2=x^2+(y-a{)}^2+z^2=x^2+y^2+(z-a{)}^2$
$\Rightarrow x=\frac{a}{2}=y=z$.Hence the required point is $(\frac{a}{2},\frac{a}{2},\frac{a}{2})$