Practice - Question 8
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Practice Questions
Test your understanding with targeted questions
Define the term 'midpoint' in your own words.
💡 Hint: Think about how you would represent the middle of a line.
What do we mean by 'distinct points'?
💡 Hint: Consider if two points can be the same.
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Interactive Quizzes
Quick quizzes to reinforce your learning
According to the pigeonhole principle, if there are five points and four pairs possible, what must be true?
💡 Hint: 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?
💡 Hint: Remember how the midpoint is calculated.
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Challenge Problems
Push your limits with advanced challenges
Provide five distinct integer-coordinate points and demonstrate their midpoints have integer values.
💡 Hint: 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.
💡 Hint: How does the pigeonhole principle apply here with various n?
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