I have always found strange that in elementary analytic geometry points are defined by their names followed by their coordinates, for example:
"Find the distance between $A(5, -3)$ and $B(2, 1)$." (source)
Usually, mathematical objects are defined either by an equality or by a uniquely characterizing property. So one would expect points to be defined such as "Let $A = (0,1)$" (once the coordinate system is fixed) or "Let $A$ be the point of coordinates $x= 0$ and $y=0$," but not "$A(0,1)$".
Furthermore, usually a letter followed by some numbers between parentheses denotes the evaluation of a function at certain points, so "$A(0,1)$" could be misunderstood for "The value of the function $A$ at point $(0,1)$".
What is the historical, practical, or whatelse reason for this notation?