How to Plot Lines Between Coordinate Pairs

I've spent quite a while searching the forums, re-reading answers, testing peoples replies and supposed solutions.... but can't get to the answer to this and it's driving me mad. A much simplified version of the problem is:

Consider two arrays: a=[1,1;1,2;1,3;1,4]

b=[2,1;2,2;2,3;2,4]

The pairs of co-ordinates are on each row, i.e. (1,1) is paired with (2,1), (1,2) with (2,2) etc. How do we join these pairs create 4 horizontal lines, without using loops.

We do NOT want a line from, e.g. (2,1) to (1,2) as this pair does not exist.

The following loop does the job: for i=1:4

plot([a(i,1),b(i,1)],[a(i,2),b(i,2)])

hold on

end

Replacing the 'i' with a ':' doesn't work, it draws two vertical lines! I'm thinking there should be a one line, vectorised answer, but I can't figure it out. Thanks in advance...