# Match off points into $N$ red/blue pairs with straight lines connecting pairs, so that none of lines we draw intersect

Suppose we are given $2N$ points in the plane (we may assume that no $3$ are collinear). Assume that $N$ of these points are colored red, and $N$ points are colored blue. Can we match off the points into $N$ red/blue pairs with straight lines connecting these pairs, so that none of the lines we draw intersect? If this matching exists, can we find it by an algorithm?

• If the matching exists we can definitely find it by looking at every possible matching. Obviously this will not be an efficient algorithm. Are there any other constraints on your algorithm? – Sean English Jan 10 '16 at 21:44
• Do the lines end at the points, or are they extended ? – true blue anil Jan 11 '16 at 12:13