17.2. Module No#08

Try these first

1. 1.

   What is the midpoint of the points (2, 3) and (4, 5)?

   Hint

   Use the midpoint formula: average the x-coordinates and y-coordinates.

2. 2.

   How many distinct points can be selected from 1 to 5?

   Hint

   Consider the numbers individually.

3. 3.

   What is the formula for calculating the midpoint between two points?

   Hint

   Recall how to calculate averages.

4. 4.

   True or False: If you pick five integers from the set {1, 2, 3, 4, 5}, there must be at least one pair that sums to six.

   • True
   • False

   Hint

   Consider the pairs available.

5. 5.

   Design a proof showing that for any arbitrary set of six integers from the range of 1 to 15, there must be at least one pair summing to 16.

   Hint

   Pair integers wisely and analyze sums.

6. 6.

   Using the midpoint formula, determine a set of five points that guarantees at least two points have integer midpoints, explaining your reasoning.

   Hint

   Group the coordinates thoughtfully.