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Why Is It Called an Ordered Pair?

Definition: Why is it called an ordered pair?

Summary

  1. The order in which we write the coordinates is VERY IMPORTANT!
  2. In the ordered pair (3,4), 3 is the x-coordinate and 4 is the y-coordinate
  3. In the ordered pair (4,3), 4 is the x-coordinate and 3 is the y-coordinate
  4. (3,4) tells us to move 3 units to the RIGHT and 4 units UP
  5. (4,3) tells us to move 4 units to the RIGHT and 3 units UP
  6. This takes us to two different points

Notes

    1. (3,4) and (4,3) are both ordered pairs
    2. They have the same numbers for their coordinates, but they're in a different order
    3. Since the numbers are in a different order, they are different points when you graph them
    1. The numbers are the same, 3 and 4
    2. The only thing different about them is the order of the numbers
    1. The x-coordinate, 3, tells us we need to move RIGHT 3 units from the origin
    2. The y-coordinate, 4, tells us we need to move UP 4 units
    1. The x-coordinate, 4, tells us we need to move RIGHT 4 units from the origin
    2. The y-coordinate, 3, tells us we need to move UP 3 units
    1. If order doesn't matter, they should be the same point
    2. But they're not!
    3. So order DOES matter!
    1. We got to different points when we plotted (3,4) and (4,3)
    2. The first coordinate tells us where to move left and right
    3. The second coordinate tells us where to move up and down
    4. So having two different first coordinates will take us to different places in the coordinate plane
    5. Same goes for different second coordinates
    1. Switching the order of the coordinates gives you a different point
    1. VERY IMPORTANT!!
    2. There's a reason 'ORDER' is in the name!!