L5 · The Cartesian plane: axes, origin and ordered pairs

Learning goal

“I can name the parts of the Cartesian plane, and I can read and write any point as an ordered pair (x, y) - across first (x), then up (y) - without ever swapping them.”

Cartesian plane — a flat grid formed by two numbered axes crossing at right angles, used to locate points.

Axis — one of the two number lines of the plane: the horizontal x-axis and the vertical y-axis; they cross at the origin.

Origin — the point (0, 0), where the x-axis and y-axis cross; every journey on the plane starts here.

Ordered pair — the pair of numbers (x, y) that locates a point: x first (distance across from the origin), y second (distance up).

Worked example

The plane for this lesson: x-axis numbered 0 to 10 across the bottom, y-axis numbered 0 to 10 up the left side; they cross at the origin (0, 0). Point P is plotted 5 across and 3 up from the origin. Step 1: Start at the origin. Count ACROSS along the x-axis: 5. That is the x-coordinate. Step 2: Count UP: 3. That is the y-coordinate. Step 3: Write the ordered pair x first, y second: P = (5, 3). Say it every time: "Across first, then up - and the pair is always written (x, y)."

Check yourself — explain it

In the ordered pair (4, 7), the number 7 tells you...

Paired problem — example still visible

Point Q is plotted 2 across and 6 up. Write its ordered pair. -> (2, 6)

Faded completion — last step is yours

"A point plotted 8 across and 1 up is written ( ___, ___ )" -> (8, 1)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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