Two number lines cross at a corner. The across one and the up one are called axes.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The crossing point has a name.
Origin is where the two axes meet. It is the point (0, 0).
An ordered pair
(3, 5) means go 3 across, then 5 up. The first number is always the across one.
Order matters
(3, 5) and (5, 3) are two different places. Swapping them puts you somewhere else.
Across first, then up
The point (3, 5) means 3 across from the origin and 5 up. The order is fixed by convention, so (3, 5) and (5, 3) are different points. Reading them in the wrong order is the single most common coordinate error.
The origin and the axes
The origin is (0, 0), where the two axes cross. The horizontal axis is the x-axis and the vertical is the y-axis. Every point is described by how far it sits along each axis, which is why two numbers are needed and no fewer.
Points on the axes
The point (4, 0) sits on the x-axis, 4 across and not up at all. The point (0, 4) sits on the y-axis. A zero coordinate is not a missing value — it says the point is exactly on that axis.
What coordinates are for
Maps, screens, graphs and games all locate things with coordinate pairs. Every pixel on this screen has a coordinate. The system is one of the most useful inventions in mathematics precisely because it turns position into arithmetic.
Step 2: Try It Yourself
Both orders are plotted, so the difference is visible rather than described.
(3, 5) and (5, 3) are two different places. The order decides which.
Step 3: Watch an Example
One step at a time.
Watch Ana Plot (4, 2)
Ana plots an ordered pair.
- Step 1
She starts at the origin.
Step 4: Your Turn
Practice makes it stick.
The Across Number
Problem 1 of 2
In the pair (7, 2), how far do you go across?
The Origin
Problem 2 of 2
How far across is the origin?
Read the Pairs
1 of 4
In (5, 9), how far up do you go?
2 of 4
In (0, 6), how far across do you go?
3 of 4
Are (2, 8) and (8, 2) the same place?
4 of 4
Are (4, 4) and (4, 4) reversed the same place?
Step 5: Quick Check
Show what you know.
Question 1 of 2
In (6, 1), how far across do you go?
Question 2 of 2
Which number comes first in an ordered pair?
What You Learned
- The axes cross at the origin, (0, 0).
- An ordered pair says how far across, then how far up.
- (3, 5) and (5, 3) are different places.