<p>This post has received a 1.99 % upvote from @booster thanks to: @droopy.</p>

I'm not sure if this is right, it's been a while but it's not possible for a fifth coordinate to exist by the rules because only four coordinates can be plotted with numbers being (odd,odd) (even,even) (odd,even) and (even,odd) and not create an integer coordinate. A fifth one would always create a full integer coordinate plot because there's only odd and even sets of numbers and finding the midpoint of any two coordinates involves dividing by two. Further, since there can only be four combinations of odd and even, one set combination would be repeated resulting in two integers. I don't remember if there's an exception so this'll be my final answer until I see otherwise.

Amazing 

Help vote my posting my best friend

My brain hurts, now I know why I'm creative and draw pictures. I'll take anotjer stab at this puzzle though.... 🤔 hmmm

You got a 0.49% upvote from @postpromoter courtesy of @droopy! Want to promote your posts too? Check out the [Steem Bot Tracker website](https://steembottracker.com) for more info. If you would like to support development of @postpromoter and the bot tracker please [vote for @yabapmatt for witness!](https://v2.steemconnect.com/sign/account-witness-vote?witness=yabapmatt&approve=1)

Your second requirement is not totally clear. For example, is it okay for the midpoint to have one integer value and one non-integer value, like (4,4.5)? or do both need to be non-integer? Just looking at each line you can tell that at least x OR y in every pair is non-integer. If both need to be non-integer, I'll need to keep working.