Coordinates
Coordinates
Coordinates are used to show the position of a point within a grid. This is very helpful to describe transformations and when points or shapes are moving around the grid.
A shape can be transformed by a reflection or a translation. We will explore these ideas in this revision page.
Compass Points
To describe direction, we can use compass points.
The 4 main compass points are north, east, south and west. There is a helpful pneumonic to help your child remember which direction the points face.
Never Eat Shredded Wheat
The compass points halfway between the main points are north-east, south-east, south-west and north-west.
Position on a Grid
Coordinates are pairs of numbers that tell you the location of a point within a grid. The first number shows the position along the x-axis (horizontal axis) and the second number shows the position along the y-axis (vertical axis).
Coordinates are written in the form (x,y)
For example point A and point B on the grid to the right have coordinates that help you locate them on the grid.
Point A: (1,2) as the point is 1 space along the x-axis and 2 spaces up the y-axis.
Point B: (5,4) as the point is 5 spaces along the x-axis and 4 spaces up the y-axis.
Example 1: Coordinates
Your child may be asked to identify the coordinates of a point on a grid.
Example: On the grid below, one line of a square has been drawn.
What are the two coordinates of the missing corner of the square?
The line of the square that is already drawn is 4 spaces along. We know that the shape is a square so the other sides need to be 4 spaces along too.
We can therefore draw the rest of the square with this information.
Now we can identify the two corner points that were missing.
(1,1) and (5,1)
Reflection
On a coordinate grid, a mirror line can be added to reflect shapes in. Each individual point of the shape and its reflected image are the same number of squares away from the mirror line.
See the example below, a triangle has been reflected in the mirror line to give a reflected image. The points of the triangle are the same distance away from the mirror line as their counterparts in the reflected image.
Translation
To translate a shape on a coordinate grid, the shape is moved across the grid without being flipped or rotated.
To find how much the shape has been translated, choose a corner then count how many squares it has moved in the horizontal direction and the vertical direction.
For example, in the grid the shape has been moved 2 squares to the right and 3 squares down.
Coordinates Example Questions
Question 1: The grid below has the map of a town on it.
What are the coordinates of:
a) Restaurant
b) Library
c) Cinema
[3 marks]
a) The restaurant is 1 square along the x-axis and 3 squares up the y-axis.
(1,3)
b) The library is 6 squares along the x-axis and 4 squares up the y-axis.
(6,4)
c) The cinema is 4 squares along the x-axis and 1 square up the y-axis.
(4,1)
Question 2: The point on the grid is moved 4 squares to the right and 2 squares up.
What are the new coordinates of the point?
[2 marks]
The current coordinate of the point is (1,1)
The new coordinate is (5,3)
Question 3: The point (4,9) is reflected in the mirror line shown on the grid below.
What are the new coordinates for the reflected point?
[1 mark]
The point (4,9) is 4 squares away from the mirror line. So, the new reflected point needs to be 4 squares away from the mirror line on the other side.
As we can see from the grid this means that the coordinates of the new reflected point is (4,1)