Ordered Pair
In short: An ordered pair is two numbers written in parentheses in a set order, (x, y), that give the exact location of a point on the coordinate plane.
6th GradeGeometry6.NS.C.6c
What is Ordered Pair?
An ordered pair is a two-part address. The first number tells the sideways move from the origin and the second tells the vertical move, so order is everything: \((4, 7)\) and \((7, 4)\) are two different spots.
Precisely, an ordered pair \((x, y)\) names the point whose horizontal coordinate is \(x\) and vertical coordinate is \(y\). Two pairs are equal only when both their first numbers and their second numbers match. Pairs also describe data, like (hours, dollars earned).
How to spot it
- Numbers appear inside parentheses separated by a comma, such as \((-2, 5)\).
- A table of inputs and outputs is read row by row as pairs.
- A question asks you to plot, read or name a point on a grid.
- A rule such as “add 3 to x” produces a list of matching y-values.
The method
- Read the first number as the x-coordinate and the second as the y-coordinate.
- Start at the origin and travel along the x-axis by the first number, then up or down by the second.
- Plot the point and label it with its pair.
- To read a pair from a graph, drop straight to the x-axis for x and straight across to the y-axis for y.
Ordered Pair: solved example
Problem
A robotics club in Dayton records the robot’s position after each move as (meters east, meters north). The robot starts at \((0, 0)\), moves 5 east and 3 south, then 2 west and 9 north. Give its final ordered pair.
Solution
After the first move: east 5, north \(-3\), so \((5, -3)\).
Second move: x becomes \(5 – 2 = 3\) and y becomes \(-3 + 9 = 6\). The final position is \((3, 6)\).
Try it
Question 1
From the origin, which pair names the point 4 units left and 9 units down?
Show the answer
\((-4, -9)\).
Question 2
A table lists the hours worked 2, 5, 8 with pay \$28, \$70, \$112. Write the three ordered pairs and the hourly rate.
Show the answer
\((2, 28)\), \((5, 70)\), \((8, 112)\). Each y divided by x is 14, so the rate is \$14 per hour.
Ordered Pair vs. Coordinate Plane
An ordered pair is the address and the coordinate plane is the map it points into. The same two numbers can describe a point on the plane or a pair of data values such as (hours, miles) in a table.
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Whole dictionary: A–Z · 6th Grade · Geometry