Answer
a) If it were in 1D, there would be only one point equidistant from $x=0$ and $x=1$, and that would be the midpoint of the line segment connecting $x=0$ and $x=1$, which is $x=\frac{1}{2}$.
In 3D, we have a set of points that are equidistant from $(0,0,0)$ and $(1,0,0)$. They take the form of a plane, which also bisects the line segment connecting $(0,0,0)$ and $(1,0,0)$. This is our conjecture.
b) Our conjecture is true.
Work Step by Step
The answer:
