This post is derived from this one.
Consider the guy pointed out by red circle the following image (img_1),
which expression in the following is more clear and idiomatic?
He is in the horizontal position.
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All of the people in the picture are in a horizontal position, so I don't think that option 1 describes his position completely.
The word supine is not very widely used: the Cambridge Dictionary describes it as formal. I knew that it meany lying down, but I was surprised to find that it does additionally mean "lying on your back, looking up". I suspect that I'm not the only one that doesn't know this. For this reason, I don't think that option 1 is very useful either.
A more idiomatic way of describing this would be:
He is lying on his back