Key takeaway: An ordered pair is two numbers written in parentheses, (x, y), where the first gives the horizontal position and the second the vertical position of a point on a coordinate plane.
Grade 66.NS.C.6cGeometry and Measurement
Definition of Ordered Pair
An ordered pair is a pair of numbers in a set order that names one point. In (4, −7), the first number says to move 4 units right of the origin, and the second says to move 7 units down.
Order matters because the two numbers play different roles. The point (4, −7) and the point (−7, 4) are in different places. Ordered pairs also record data, such as (hours worked, dollars earned), where each pair links two related values.
Formula and notation
The numbers go in parentheses separated by a comma:
\[(x,\, y)\]
The first number \(x\) is the x-coordinate, the second \(y\) is the y-coordinate. A move of \(a\) units right and \(b\) units up changes \((x,\, y)\) to \((x + a,\, y + b)\); negative values mean left or down.
Key facts
- Swapping the two numbers usually gives a different point.
- The origin is the ordered pair (0, 0).
- Each point of the plane matches exactly one such pair, and each pair matches one point.
- In a table of values, every row can be written as a pair to graph.
Ordered Pair example
On a treasure map, a ship sits at \((4,\, -7)\). It sails 9 units up and 5 units left. Where does it end up?
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Moving up changes the second number: \(-7 + 9 = 2\).
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Moving left changes the first number: \(4 – 5 = -1\).
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The new location is \((-1,\, 2)\).
The ship ends at \((-1,\, 2)\), in the upper left region of the map.
Common mistake
Watch out
Dara says \((3,\, 8)\) and \((8,\, 3)\) name the same point because they use the same two numbers.
Why it is wrong
The first number is always the horizontal position. \((3,\, 8)\) is 3 right and 8 up; \((8,\, 3)\) is 8 right and 3 up. They are different points, mirror images across the line where \(y = x\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement