I did this question by identifying integral points on the line that would be nearest to the points given in options.

For ex. (2,-1) would be nearest to integral points (2,2) or (-1,-1) on the line x=y.

This distance seems to be more (because 1 coordinate is 3 units away from the point on the line) than distance of the point (2,1) from nearest integral points on the line such as (2,2) or (1,1).

Similarly, I eliminated the remaining choices.

You may verify by applying the distance formula.

Please give a kudos if this helps.