Transformations
Coordinates and translations
Coordinates tell you exactly where a point is on a grid. A translation slides a shape to a new place without turning or flipping it.
Reading and writing coordinates
A pair of coordinates is written (x, y). The x-axis number comes first (how far across) and the y-axis number comes second (how far up or down). Coordinates can be positive or negative, depending on where they are on the grid, and they do not always have to be whole numbers.
Which way to move
The signs tell you the direction from the origin (0, 0): ā¢ (+, +) ā right, up ā¢ (+, -) ā right, down ā¢ (-, +) ā left, up ā¢ (-, -) ā left, down
Translating a shape
To translate a shape, move every vertex the same number of squares in the same direction. ā¢ Right adds to x; left subtracts from x. ā¢ Up adds to y; down subtracts from y. A vertex and its new position are called corresponding vertices, often labelled A and A' (A dash).
Completing a shape
If you know some of the vertices of a square, rectangle or other shape, you can use the coordinates to work out the missing vertex ā its x and y line up with the corners you already have.
Worked examples
Reading a point's coordinates
- Find how far the point is across: 3 squares right, so x = 3.
- Find how far up it is: 2 squares up, so y = 2.
- Write the x number first, then the y number.
Answer: The point is (3, 2).
Translating a triangle 4 left and 2 down
- Move each vertex 4 squares left and 2 squares down.
- Vertex A (1, 1): 1 ā 4 = -3 and 1 ā 2 = -1.
- Do the same for B (4, 3) and C (2, 4).
Answer: A' (-3, -1), B' (0, 1) and C' (-2, 2).
Describing a translation
- Compare the x-coordinates: 1 goes to 5, that is 4 to the right.
- Compare the y-coordinates: 1 goes to 4, that is 3 up.
Answer: The translation is 4 squares right and 3 squares up.
Finding a missing vertex
- Three corners of a square are (2, 3), (5, 3) and (2, 6).
- The fourth corner shares x = 5 with (5, 3) and y = 6 with (2, 6).
Answer: The missing vertex is (5, 6).
Where you see this in real life
- Reading a treasure map to find the coordinates of the chest.
- Orienteering, where you read coordinates to move between check points.
- Moving a shape or spaceship around a computer-game grid.
Key words
- Coordinates
- A pair of numbers (x, y) that give the position of a point on a grid.
- Axes
- The two number lines on a grid: the x-axis across and the y-axis up.
- Origin
- The point (0, 0) where the two axes cross.
- Translate
- To slide a shape to a new position without turning or flipping it.
- Corresponding vertices
- Matching corners of a shape before and after it is moved, such as A and A'.