GIMP :: Drawing A Line Within A Shape

How do you draw a line within a shape? I know how to make a circle or rectangle (through the circle or rectangle select tool/stroke path) and how to draw straight lines. I want to take a box like this:

-----
1 1
1 1
1 1
-----

and add a line through the center like this:

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1 1
1-----1
1 1
-----

And of course I'd prefer the line be neat, from one end of the shape to the other, not just a sloppily drawn line.

Of course I can do this very slowly by drawing the line, zooming way in, and manually moving the line into place. But surely there's a better way!