Prove that a point $X$ determine it's coordinates uniquely.
My answer: Let $X$ be a point in the plane with coordinates $(x_1,x_2,x_3)$. Suppose that X can also be determined by the coordinates $(y_1,y_2,y_3)$.
The distance between X and X is given by $\sqrt{(x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2} \neq 0$ since both sets of coordinates are not equal to zero, but this is a contradiction given that the distance between $X$ and $X$ should be zero since it's the same point.
Therefore $X$ is determined by one and only one set of coordinates.
Is this proof right?