Coordinates & Translation
Reading and plotting coordinates in all four quadrants, and translating shapes on a grid.
What is Coordinates & Translation?
Coordinates describe the position of a point on a grid using two numbers: the x-coordinate (horizontal position) and the y-coordinate (vertical position), written as (x, y).
In the 11+ exam, you may need to read and plot coordinates, work in all four quadrants (including negative numbers), translate shapes, and find midpoints.
Step-by-Step Method
Remember: x first, y second
Coordinates are always written (x, y). Think “along the corridor, then up the stairs”.
For negative coordinates, go left or down
Negative x = go left. Negative y = go down. The four quadrants are: (+,+), (-,+), (-,-), (+,-).
For translation, add the movement to each coordinate
Moving right adds to x. Moving up adds to y. Moving left subtracts from x. Moving down subtracts from y.
For midpoints, average the coordinates
Midpoint = ((x1 + x2)/2, (y1 + y2)/2). Add the x-coordinates and divide by 2, same for y.
Plot carefully on the grid
Always start from the origin (0,0). Go along the x-axis first, then up or down on the y-axis.
Worked Examples
Plot the point (-3, 2).
Working
- Start at the origin (0, 0).
- x = -3: move 3 squares to the LEFT.
- y = 2: move 2 squares UP.
A triangle has a vertex at (2, 5). It is translated 4 right and 3 down. What are the new coordinates?
Working
- 4 right: add 4 to x-coordinate: 2 + 4 = 6.
- 3 down: subtract 3 from y-coordinate: 5 – 3 = 2.
- New coordinates: (6, 2).
Find the midpoint of (2, 6) and (8, 2).
Working
- x-midpoint: (2 + 8) / 2 = 10 / 2 = 5.
- y-midpoint: (6 + 2) / 2 = 8 / 2 = 4.
Common Mistakes
Getting x and y the wrong way round (going up first, then along).
x is ALWAYS first (horizontal). y is ALWAYS second (vertical). Along the corridor, then up the stairs.
Forgetting the negative sign in quadrants with negative coordinates.
If the point is to the left of the y-axis, x is negative. Below the x-axis, y is negative.
Adding instead of subtracting for leftward or downward translations.
Left = subtract from x. Down = subtract from y. Right = add to x. Up = add to y.
Top Tips
- Remember the phrase “along the corridor, then up the stairs” for (x, y) order.
- When translating a shape, apply the same movement to EVERY vertex, then redraw.
- The midpoint formula is just the average of the x-values and the average of the y-values.
- In all four quadrants, the signs are: top-right (+,+), top-left (-,+), bottom-left (-,-), bottom-right (+,-).
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions