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Academy11+

11+ Maths · Topic explained

Coordinates

How do you tell a friend exactly where the treasure is buried?

The big idea

A coordinate (x, y) means: go along x, then up y.

Picture it

Along the corridor, then up the stairs.

Key words

x-axis
The line going across, along the bottom.
y-axis
The line going up the side.
origin
The point (0, 0), where the axes meet.

Worked examples

  1. 1Warm-up

    Plot the point (2, 5).

    • Start at (0, 0)
    • Go 2 along, then 5 up
  2. 211+ standard

    Three corners of a square are (1, 1), (1, 4) and (4, 4). Find the fourth corner.

    • The sides are 3 squares long
    • The missing corner is under (4, 4), level with (1, 1)
    • Fourth corner: (4, 1)
  3. 311+ standard

    What point is exactly halfway between (2, 5) and (8, 5)?

    • Same y, so stay at y = 5
    • Halfway between 2 and 8 is 5
    • Midpoint: (5, 5)
  4. 411+ standard

    The point (3, 2) moves 4 right and 1 down. Where does it end up?

    • Right adds to x: 3 + 4 = 7
    • Down takes from y: 2 − 1 = 1
    • New point: (7, 1)

The common mistake

The mistake

(3, 5) means 3 up and 5 along.

Instead

x comes first: 3 along, then 5 up.

Why: The order matters: (3, 5) and (5, 3) are different points.

Where it comes up in the 11+

Read and plot points, find a missing corner of a shape, and move (translate) points.

The video

Video coming soon

We're making a short video that explains coordinates step by step. Until then, everything it covers is on this page.

Free printable

Coordinates worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. What is the point (0, 0) called?

    • The axis
    • The origin
    • The vertex
    • The centre
    Show the answer

    The origin

    The origin is where the x-axis and y-axis meet.

  2. 2. Which point lies on the x-axis?

    • (0, 4)
    • (4, 0)
    • (4, 4)
    • (1, 1)
    Show the answer

    (4, 0)

    Points on the x-axis have a y-coordinate of 0.

  3. 3. A rectangle has corners at (2, 1), (6, 1) and (6, 3). Where is the fourth corner?

    • (2, 3)
    • (3, 2)
    • (6, 6)
    • (2, 6)
    Show the answer

    (2, 3)

    Above (2, 1) and level with (6, 3): x = 2, y = 3.