Practice Midpoint Of The Line Joining Points (17.5.1) - Module No#08 - Discrete Mathematics

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6 sample questions

Question 1.
Calculate the midpoint of the points (1, 1) and (3, 3).
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Sum the x-coordinates and y-coordinates separately and divide by 2.
Question 2.
What can you infer about the midpoint of (5, 7) and (5, 9)?
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Examine the x-coordinates; they are identical.
3Question 3.
What is the midpoint of (3, 4) and (5, 8)?
- (4
- 6)
- (3.5
- 6)
- (6
- 10)
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Remember the midpoint formula.
4Question 4.
Applying the pigeonhole principle, how many odd points do we need to guarantee at least two share the same characteristic?
- 3
- 4
- 5
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Think about the maximum characteristics available.
Question 5.
If you select any five integer-coordinate points from (1,1) to (8,8), construct a proof showing at least one pair will have an integer midpoint.
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Always categorize the points based on parities first.
Question 6.
Consider points at the corners of a square. Calculate their midpoints and verify whether they yield integers.
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Pairs to consider are (x1, y1) with (x2, y2) opposite.

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