Year 5 · Position and direction
Read and mark points on a grid
Learn how to read and mark coordinates, describe a slide by how the coordinates change, find lines of symmetry, and reflect shapes in horizontal and vertical lines.
Definition
Coordinates give a point on a grid an exact address: two numbers in brackets, with the across number first and the up number second, both counted from the origin (0, 0). Once every corner of a shape has an address, you can say exactly where the shape is, slide it to a new place, and describe that move by how the numbers change. A grid also makes mirror lines easy to work with: a shape can be reflected across a horizontal or vertical line, square by square.
Why Do I Have to Learn This?
Coordinates pinpoint an exact spot using two numbers. Maps, video games and treasure hunts all rely on them.
Key Rules:
- 1. Read or mark a point across first, then up: (3, 2) means 3 along from (0, 0), then 2 up.
Remember:
- •Across first, then up. A slide changes every coordinate by the same amount; a reflection mirrors each point at the same distance from the line.
Don’t Forget...
- •Swapping the two numbers and plotting (3, 5) as 5 across and 3 up. Coordinates always read across first, then up, so (3, 5) and (5, 3) are two different points on the grid.
- •Reflecting a shape by sliding it across the mirror line without flipping it. A reflection turns the shape over: a corner 2 squares to the left of the line lands 2 squares to the right, so the image faces the opposite way to the original.
- •Changing the y-coordinate when a slide says right or left. Right and left change the first number and up and down change the second, because across always comes first in a coordinate pair.
Axis (axes)
The numbered lines running across and up a graph.
The bottom axis shows the days and the side axis shows how many books were read.
Worked Example:
Three corners of a rectangle are at (1, 2), (5, 2) and (5, 4). Find the coordinates of the fourth corner.
Plot each point across first, then up.
(1, 2) and (5, 2) are level with each other, so they make the bottom side of the rectangle.
(5, 4) sits directly above (5, 2), so the top side must be level at a height of 4.
The fourth corner sits directly above (1, 2) at that same height: 1 across, 4 up.
Answer: (1, 4)
Why It Works:
Two numbers fix one exact point, because counting across and then up from (0, 0) can only land in one place. A slide changes every coordinate by the same amounts because the whole shape moves together without turning, and a reflection keeps each point the same distance from the mirror line, which is exactly what makes the two halves match.
Another Example:
A triangle has corners at (2, 1), (4, 1) and (3, 3). Slide it 3 squares right and 2 squares up, and give the new coordinates.
Sliding 3 right adds 3 to every x-coordinate, and sliding 2 up adds 2 to every y-coordinate.
(2, 1) becomes (2 + 3, 1 + 2), which is (5, 3).
(4, 1) becomes (7, 3), and (3, 3) becomes (6, 5).
Check: the new triangle is the same size and the same way up, just in a new place.
Answer: (5, 3), (7, 3) and (6, 5)
Animated Example:
Free Read and mark points on a grid Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Position and direction (Year 4) · Next: Position and direction (Year 6)
Let’s Practise the Concept
Step 1 of 3
Put them in order
Tap the numbers from smallest to largest.
In order so far: nothing yet