An ordered pair (x, y) names a position on a graph. To plot it, start at the origin, go across by x, then up or down by y.
How do you plot a point?
Use the across-then-up rule. The x value comes first in the brackets and first in the movement.
Positive x moves right and negative x moves left. Positive y moves up and negative y moves down.
Worked example
Plot the original points A(−3, 2), B(1, 2), C(1, −2) and D(−3, −2), then join them in order.
| Point | Start at origin | Move |
|---|---|---|
| A(−3, 2) | (0, 0) | 3 left, 2 up |
| B(1, 2) | (0, 0) | 1 right, 2 up |
| C(1, −2) | (0, 0) | 1 right, 2 down |
| D(−3, −2) | (0, 0) | 3 left, 2 down |
Joining A to B to C to D and back to A gives a four-sided shape. The top side AB is 1 − (−3) = 4 units long, and the side BC is 2 − (−2) = 4 units high. So the shape is a square with sides of 4 units.
If the picture is not a square, one of the four points is wrong, and that is how you find it.
What does the common mistake look like?
A student plots (2, 5) by going 5 across and 2 up, which is the point (5, 2). The pair was read in the wrong order. On a graph where the points should form a line, this point sits noticeably off the line.
The fix is to say the movement aloud: “across 2, up 5”. Another habit is to write (x, y) above the brackets on your rough work until the order is automatic.
A second common slip is to count the origin as 1 when counting along an axis. Start counting from the next mark after the origin, not from the origin itself.
Steps to follow
- Put your pencil on the origin.
- Move along the x-axis by the first number, left if negative.
- Move parallel to the y-axis by the second number, down if negative, then mark the point with a small cross.
Self-check
Plot E(−2, 3), F(0, −1) and G(4, 3). State which two points share the same y value and what the distance between them is.
Answer
E is 2 left and 3 up. F is on the y-axis, 1 below the origin. G is 4 right and 3 up.
E and G both have y = 3, so they are on the same horizontal line. The distance between them is 4 − (−2) = 6 units. The subtraction of a negative is where students often slip.
Where to go next
Once points land where they should, learn to fit them on paper with choosing axes and scales. The linear law axes explorer gives extra plotting practice, and the coordinates and gradients hub shows the full sequence.