Position and direction
Coordinates
A pair of numbers pins down an exact point on a grid. Always read along the bottom first, then up.
Reading a coordinate pair
A point on a grid is described by two numbers in brackets, like (3, 5). The FIRST number is how far ACROSS (the x-axis). The SECOND number is how far UP (the y-axis). So (3, 5) means 3 across and 5 up. The order matters: (3, 5) and (5, 3) are different points.
Along the corridor, then up the stairs
A useful way to remember the order: go along the corridor, then up the stairs. Always start at (0, 0) — the ORIGIN, in the bottom-left corner. Count across first, then up. Swapping the two numbers is the commonest mistake in this topic.
Plotting a point
1. Start at the origin. 2. Count across to the first number. 3. Count up to the second number. 4. Mark the point clearly. Mark it with a small cross or dot exactly where the grid lines meet — not in the middle of a square.
Finding a missing vertex
Coordinates let you work out shapes. Three vertices of a rectangle are (1, 3), (1, 2) and (4, 2). Where is the fourth? In a rectangle the sides are parallel, so the missing point must share an x-value with (4, 2) and a y-value with (1, 3). That gives (4, 3). Plotting the three you know makes the fourth obvious.
Worked examples
Reading the point (3, 5)
- The first number is across: 3.
- The second number is up: 5.
Answer: 3 across and 5 up
Are (3, 5) and (5, 3) the same?
- (3, 5) is 3 across and 5 up.
- (5, 3) is 5 across and 3 up.
- They are in different places.
Answer: No — the order matters
The fourth vertex of a rectangle
- Three corners are (1, 3), (1, 2) and (4, 2).
- The missing corner lines up above (4, 2) and across from (1, 3).
Answer: The fourth vertex is (4, 3)
Where is the origin?
- The origin is where the two axes meet.
- It is the bottom-left corner of the grid.
Answer: The origin is (0, 0)
Plotting (0, 4)
- The first number is 0, so do not move across at all.
- The second is 4, so go 4 up.
Answer: It sits on the y-axis, 4 up
Where you see this in real life
- Map references use coordinates to pinpoint a location.
- Games like Battleships work by naming grid squares.
- Seat numbers in a theatre work like coordinates: row and seat.
Key words
- Coordinates
- A pair of numbers giving an exact position on a grid.
- x-axis
- The horizontal axis, going across.
- y-axis
- The vertical axis, going up.
- Origin
- The point (0, 0) where the axes meet.
- Plot
- To mark a point on a grid.
- Vertex
- A corner of a shape.