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“ALL steps must be shown:

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.

N.B. You must prove this in general, not just for one specific case. I.e.: describe the process someone would take that given any thousand points, he or she could draw a line that divides them into two halves.

Show all steps used to obtain the answer.”

The only thing I got out of this problem was that I had to consider the slopes of the lines determined by each pair of points, and my teacher said that was true. I didn't get much further, though. I tried finding a mean point and slope, but that didn't work out too well. How would one even make sure that such a "mean line" would not hit any existing points?!

The only help I found online was calculus-level, and I'm a freshman (and no math whiz!). Please help!

Thank you,

Alisa

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# Homework Help: One Line, a Thousand Points

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