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Show a pair has a midpoint with integer coordinates

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Let p = {(x1, y1), (x2, y2), (x3, y3), (x4, y4), (x5, y5)} be a set of five distinct points in the plane , each of which has integer coordinates. Show that some pair has a midpoint that has integer coordinates.

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Solution Summary

The expert shows a pair on the midpoint with integer coordinates. A set of five distinct points in the plane are determined.

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In order for a pair to have integer co ordinates , the sum of the pair should be even ( mid point = (x1 +x2)/2.

Now : even + even = even
odd + odd = even
...

Solution provided by:
Gaurav Agarwal, MS
Education
  • BE, Bangalore University, India
  • MS, University of Wisconsin-Madison
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