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3 cards from this section. Quick, good the night before a test.
Define the term 'midpoint' in your own words.
Think about how you would represent the middle of a line.
What do we mean by 'distinct points'?
Consider if two points can be the same.
According to the pigeonhole principle, if there are five points and four pairs possible, what must be true?
Think about how many types of bins you have versus items.
If the midpoint of two points is (2, 2), what can you say about the coordinates of those points?
Remember how the midpoint is calculated.
Provide five distinct integer-coordinate points and demonstrate their midpoints have integer values.
Use the midpoint formula for your calculations.
Mathematically prove that among n distinct points defined on integer coordinates, where n > 4, there exists an integer midpoint.
How does the pigeonhole principle apply here with various n?
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