Should the added point have integral coordinates or it doesn’t matter???
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I was not in a position to answer this question, a few minutes back, since I myself couldn’t submit the correct solution. :-/
But I think I can answer this now 
The added point need not have integral co-ordinates
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Same here. I had to assume that for solving and getting ac. My bad I forgot to update it here. The confusion arose because it was given set of integral coordinates and including non integral coordinates in it seemed absurd.
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Yes I can see now why everyone is getting confused. My answer was wrong. I have deleted it now so that it wont mislead others 
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I have no idea why this is upvoted, but requirement for integral coordinates is not valid…