You're given a grid with a point marked on it. Your job is to write down its coordinates — a pair of numbers (x, y) that says exactly where the point sits.
The two-step method
Find how far the point is from the origin along the x-axis (to the right). That's the x-coordinate.
Find how far the point is above the x-axis (going up). That's the y-coordinate.
Write the pair as (x, y) — x first, y second.
The trick: drop a vertical line from the point down to the x-axis, and read the number where it lands. Then drop a horizontal line from the point across to the y-axis, and read that number.
A worked example
A point is marked 5 squares to the right of the origin and 3 squares up. What are its coordinates?
x-coordinate: 5 (5 squares right).
y-coordinate: 3 (3 squares up).
Coordinates: (5, 3).
Another point sits directly above the 2 on the x-axis, four gridlines up. What are its coordinates?
x = 2, y = 4.
Coordinates: (2, 4).
Points on the axes
Points that sit on an axis have one coordinate equal to 0.
A point on the x-axis, three squares to the right of the origin: (3, 0) — y is 0 because it didn't go up at all.
A point on the y-axis, two squares above the origin: (0, 2) — x is 0 because it didn't go right.
The origin itself: (0, 0).
Common mistakes
Swapping the order. (3, 5) is not the same as (5, 3). Always x first, y second. The mnemonic "along the corridor, then up the stairs" helps — you walk before you climb.
Counting from the wrong line. Always count from the origin (0, 0), not from the edge of the page or any random gridline.
Off-by-one when counting gridlines instead of squares. Count the gridlines you cross, not the squares between them. The first gridline to the right of the origin is x = 1, the second is x = 2, and so on.
Forgetting the brackets and the comma. A coordinate is (3, 5), not "3 5" or "3-5".
A puzzle
Three points sit at (1, 1), (1, 4) and (5, 1). If you join them with straight lines, what shape do you get?
(1, 1) is one square right, one up.
(1, 4) is one square right, four up — directly above (1, 1).
(5, 1) is five right, one up — directly to the right of (1, 1).
Joining them, you get a right-angled triangle with the right angle at (1, 1). The two short sides are 3 squares and 4 squares.
