A thousand points are graphed in the coordinate plane. Explain why it is possible to draw a straight line in the plane so that half of the points are on one side of the line and half are on the other.

Hint: Consider the slopes of the lines determined by each pair of points.

So how would I do this? I found this but I don't really understand it so it's not much help for me:
http://www.physicsforums.com/showthread.php?t=65986

Question

A thousand points are graphed in the coordinate plane. Explain why it is possible to draw a straight line in the plane so that half of the points are on one side of the line and half are on the other.

Hint: Consider the slopes of the lines determined by each pair of points.

So how would I do this? I found this but I don't really understand it so it's not much help for me:
http://www.physicsforums.com/showthread.php?t=65986

anonymous · Answer

I answered this for Courtney.

anonymous · Answer

http://openstudy.com/users/estudier#/users/estudier/updates/4e324eb30b8ba7b2da4168d5

anonymous · Answer

ok I get that but do you think there is a way to do it using the slopes?

anonymous · Answer

Well, I am using slopes (perpendiculars) but not per pair, what is the rule for associating a pair with another pair, there are 999 candidates?

anonymous · Answer

um... I don't know

anonymous · Answer

It's obviously something to dp with curve fitting/least squares, that sort of thing, don't know how to explain it though.

anonymous · Answer

hmm ok well thanks for helping :)

anonymous · Answer

ur welcome, I will give it some more thought, see if I can divine what the "helpful hint" is supposed to mean:-)