Extracting first and second coordinates of an ordered pair

I’m trying to find a way to extract coordinates from an ordered pair in TeX. See this example code.

documentclass[12pt]{article}
usepackage{xparse}
begin{document}

% #1 and #2 are ordered pairs
NewDocumentCommand{coord}{ m m }
{
#1, #2

% Ordered pairs which correspond to (a) first coordinate of first pair and second 
% coordinate of second pair, (b) second coordinate of first pair and first coordinate of 
% second pair.

(#1[1], #2[2]), (#1[2]. #2[1])
}

coord{(1, 2)}{(3, 4)}

end{document}

The expected output from coord{(1, 2)}{(3, 4)} would be

(1, 2), (3, 4)
(1, 4), (2, 3)

defcoord#1#2{coordA#1#2}
defcoordA(#1,#2#3)(#4,#5#6){par(#1, #2#3), (#4, #5#6)par(#1, #5#6), (#4, #2#3)par}

coord{(1, 2)}{(3, 4)}