The x-axis and y-axis cross at the origin, (0, 0), and split the grid into four quadrants numbered anticlockwise from the top right. A coordinate pair is written (across, up or down). Right and up are positive, and left and down are negative. So (−2, 3) is 2 left and 3 up, in Quadrant 2. To move a point, change only the coordinate for that direction: right or left changes x, and up or down changes y. Moving right adds to x and moving left subtracts, so (−2, 3) moved 4 right is (2, 3).
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- quadrant
- one of the four regions the axes split a grid into
- origin
- the point (0, 0) where the axes cross
- x-coordinate
- the first number, how far across
- y-coordinate
- the second number, how far up or down
Worked examples
Point P is 3 left of the origin and 2 up. What are its coordinates?
- 1.Left is negative, so x = −3.
- 2.Up is positive, so y = 2.
- 3.P is (−3, 2).
= (-3, 2)
Which quadrant is the point (4, −1) in?
- 1.x = 4 is right of the y-axis.
- 2.y = −1 is below the x-axis.
- 3.Right and below is the bottom right, Quadrant 4.
= Quadrant 4
Point P is at (−2, 3). It moves 4 units to the right. What are its new coordinates?
- 1.Moving right changes x only: −2 + 4 = 2.
- 2.The y-coordinate stays 3.
- 3.P is now (2, 3).
= (2, 3)
A, B and C are three corners of a rectangle with sides parallel to the axes: A (−4, 1), B (3, 1), C (3, −2). What are the coordinates of the fourth corner D?
- 1.D is directly below A, so it has A's x-coordinate: −4.
- 2.D is level with C, so it has C's y-coordinate: −2.
- 3.D is (−4, −2).
= (-4, -2)
For parents
Method: Across, then up or down
What to say: Start at the origin. Which way does the first number take us? Is that left or right? Then which way does the second number take us?
Common mistakes:
- Swaps the order of the coordinates, reading or plotting up before across.
- Gets the sign of the x-coordinate wrong: treats left as positive or right as negative.
- Gets the sign of the y-coordinate wrong: treats down as positive or up as negative.
- Moves the wrong way along an axis: adds when going left or down, or subtracts when going right or up.
- Applies a move across to the y-coordinate, or a move up or down to the x-coordinate.
- Ignores the negative sign on the starting coordinate, so crossing an axis goes wrong.