Finding places on a grid
Maps, games like Battleship and computer screens all use grids to describe locations. In maths, we name each point with an ordered pair (x, y).
Parts of the grid
- The x-axis runs across (horizontal).
- The y-axis runs up (vertical).
- They meet at the origin, (0, 0).
Reading an ordered pair
In (4, 3):
- The x-coordinate is 4: move 4 across.
- The y-coordinate is 3: move 3 up.
The order matters! (4, 3) and (3, 4) are different points.
Memory trick: "Along the corridor, then up the stairs." Or: x comes before y in the alphabet.
How to plot a point
- Start at the origin.
- Move right by the x-coordinate.
- Move up by the y-coordinate.
- Draw a dot and label it.
| Point | Across | Up |
|---|---|---|
| A (2, 5) | 2 | 5 |
| B (6, 1) | 6 | 1 |
| C (0, 4) | 0 (stay on y-axis) | 4 |
| D (3, 0) | 3 | 0 (stay on x-axis) |
Points on the axes
- A point with x = 0 is on the y-axis: (0, 4).
- A point with y = 0 is on the x-axis: (3, 0).
Drawing shapes from points
Plot points and join them in order to draw a shape.
Example: Plot (1, 1), (5, 1), (5, 4), (1, 4) and join them. You get a rectangle 4 units wide and 3 units tall.
Finding the coordinates of a point
Go straight down from the point to the x-axis to read x. Go straight across to the y-axis to read y.
Worked examples
Example 1: Plot (3, 7).
Start at (0, 0), go 3 right and 7 up.
Example 2: A point is 5 right and 2 up from the origin. Write its ordered pair.
(5, 2).
Example 3: Three corners of a square are (2, 2), (6, 2) and (6, 6). Find the fourth.
(2, 6).
Common mistakes
- Going up first, which swaps x and y.
- Counting grid squares instead of grid lines. Points sit where lines cross.
- Forgetting that 0 means stay on the axis.
Try it yourself
- In (8, 3), what is the y-coordinate?
- Which point is on the x-axis: (0, 5) or (5, 0)?
- What are the coordinates of the origin?
- Plot (1, 2), (4, 2) and (1, 6). What shape do they make when joined?
Answers: 1) 3 2) (5, 0) 3) (0, 0) 4) a right triangle
Quick recap
- An ordered pair (x, y) names a point.
- Move across by the x-coordinate, then up by the y-coordinate.
- Start from the origin every time you plot.