Maths: coordinates on a grid

Watch it happen

Slide a triangle across the grid

The grid. Coordinates are written (across, up): across first — along the corridor, then up the stairs.

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The idea

A coordinate pair (x, y) gives a position on a grid: the first number is how far along (horizontally), the second is how far up (vertically). Remember it as 'along the corridor, then up the stairs' — x always comes first.

A translation slides a shape without turning or flipping it. 'Right 3' adds 3 to every x-coordinate; 'down 1' subtracts 1 from every y-coordinate. Every point of the shape moves by exactly the same amount.

When a whole shape is translated, work out the new position of one corner at a time — or just translate one corner and redraw the same-sized shape from it.

Worked example

The triangle has vertices P (4, 4), Q (6, 4) and R (4, 7). The triangle is translated 2 to the left and 1 up. What are the coordinates of point P after the translation?

1. Read the starting triangle off the grid: P is at (4, 4), Q is at (6, 4), R is at (4, 7). (x first, then y — along the corridor, then up the stairs.)

   

2. Every point slides the same way: 2 to the left and 1 up. The dashed outline in the second picture shows where the whole triangle is heading — a translation never turns or flips the shape.

   

3. Vertex P starts at (4, 4). Add the slide: (4 − 2, 4 + 1) = (2, 5), exactly where the last picture shows it.

   

Answer: P moves to (2, 5).

Try one yourself

Same triangle, same slide (2 to the left and 1 up). Where does vertex Q end up?

Watch out

• Swapping the coordinates and writing (y, x) — x always comes first.
• Adding for a move down or subtracting for a move up.
• Moving only one corner of a shape and distorting it — every point moves identically.