Line segments between points in a plane

Hey everyone, I was hoping someone might be able to help point me in the right direction with a proof I'm trying to figure out.

Let's say I have an even number of points in a plane such that no three points are collinear. Now let's say each point is randomly assigned a number of either 1 or 2 such that half of the points are 1's and half of the points are 2's.

I need to prove that it's always possible to pair up each 1 point with a 2 point by drawing a line segment between them such that no two line segments intersect.

Does anyone know the best way to approach this?

I was trying to figure out a way to do a proof by induction, but I'm not sure how that would work. Maybe a proof by contradiction?

Any help is much appreciated. Thanks!

Re: Line segments between points in a plane

HI, to me induction seem a good way, you show that you can always do it (Let's say with 4 point) than you prove that if you had 2 random point, it alwasy be like solving the one with n-2 point?

I've not tryed it. But to me it seem like a good way to do it.