Reading coordinates

Reading coordinates

Reading coordinates

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

  1. Find how far the point is from the origin along the x-axis (to the right). That's the x-coordinate.
  2. Find how far the point is above the x-axis (going up). That's the y-coordinate.
  3. 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.

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