identify cluster [closed]

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I have following vector

{Point(100, 200), Point( 101, 202 ), Point ( 200, 200 ), ( 201, 202 ), ( 203, 204 ), Point ( 100, 400 ), Point( 102, 402 ), Point ( 200, 400), Point ( 202, 401 ), ( 205, 405 ) }

The vector contains vertices of a rectangle and some neighboring points of vertices. I need to extract the rectangle vertices from these points. means for Point ( 100, 200 ) and ( 101, 102 ) I just need one of them. Then for Points ( 200, 200 ), ( 201, 202 ) , ( 203, 204 ) I just need one point ( may be average or center of these neighbors ) and so forth. It may be a triangle with similar distribution or just a line with two groups or a point with a single group. Kindly guide me how can I achieve this? Should I use Kmeans or if yes how? if not is there any other clustring algorithm to solve this issue.