One number is never enough to say where something is on a flat surface. You need two: how far across, and how far up. Write them in a bracket with the across one first, and you have a coordinate.
A cinema ticket says row H, seat 12. A chessboard square is called e4. In every case it takes two numbers, one for each direction, and everybody understands that swapping them would send you to the wrong place.
The words you need
| Word | What it means |
|---|---|
| x-axis | The horizontal line, running across. It carries the first number |
| y-axis | The vertical line, running up. It carries the second number |
| Origin | Where the two axes cross. It is (0, 0) and every journey starts there |
| x-coordinate | The first number in the bracket. How far across from the origin |
| y-coordinate | The second number. How far up from where you stopped going across |
| Ordered pair | The two numbers together, in a bracket, in the fixed order (x, y) |
The point (3, 2) and the point (2, 3) are different places. The phrase to say in your head every time is: along the corridor, then up the stairs. You always walk along before you climb, and x always comes before y.
Plotting a point
To plot (5, 3): start at the origin, count 5 units across to the right, then 3 units straight up. Always start at the origin, never from the last point you plotted.
A point like (4, 0) has not gone up at all, so it sits on the x-axis. A point like (0, 4) has not gone across, so it sits on the y-axis. Zero is not a missing number here, it is a real instruction that says do not move in that direction.
Distance between two points on a line
If two points have the same y-coordinate, the distance between them is the difference in their x-coordinates. From (2, 5) to (9, 5) is 7 units. If they share an x-coordinate, use the difference in the y-coordinates instead.
Coordinates are the bridge between geometry and algebra. Once a point is a pair of numbers, a shape becomes a list of pairs and a line becomes a rule connecting x to y. Every graph you meet later sits on the two axes you are learning to use now.
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Plot A(2, 1), B(6, 1), C(6, 4) and D(2, 4). What shape is ABCD, and what is its area?
P(1, 3), Q(1, 8) and R(5, 3) are three corners of a rectangle. Find the fourth.
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It takes two numbers to name a point on a flat surface: how far across, and how far up.
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