How to understand Coordinates
Introduction
Coordinates show you the position of a point using exact values. Coordinates are represented on a graph with a x (horizontal) and y axis (vertical).
In order to reach the red circle you need to move from the origin (0), go 4 units horizontally and then 2 units vertically. This distance can be expressed as a coordinate which would be written as (4, 2).
It is important to remember that you always go horizontally first and then vertically.
If you have to plot the point (6, 1) then you would, from 0, go 6 units horizontally and then 1 unit vertically and this is shown by the black circle on the diagram above.
You should also be aware that coordinates can take negative values also and not just positive values. Negative x coordinates go left from 0 and negative y coordinates go downwards from 0.
Coordinates - Example 1
Take a look at the following question:
To find the coordinates of P you must always start at 0. Here you need to go 3 units horizontally and then 2 units vertically. The coordinates of P are (3, 2)
b i) here you simply need to go 3 units horizontally and this is shown by the red circle on the diagram.
b ii) to plot (-2, -3) you need to first go 2 units to the left horizontally and then from -2 you need to go 3 units vertically downwards. This is shown in the diagram in blue.
Coordinates - Example 2
Take a look at the following question:
To find the mid-point of a line PQ you need to take the average of the x and y coordinates.
The average of the x coordinates is \frac{7+1}{2}=4
The average of the y coordinates is \frac{10+2}{2}=6
So the coordinates of the midpoint are (4, 6).
Coordinates – Question Practice
Try the following questions on your own before looking at the solution:
Coordinates – Question Practice Solutions
The mid-point of the line is the average of the x and y coordinates.
Average of the x coordinates = \frac{1+5}{2}=3
Average of the y coordinates = \frac{4+0}{2}=2
The coordinates of the midpoint are (3, 2).
Coordinates Question Practice
Coordinates Question Practice Solutions
- P has the coordinates (4, 3). Remember you must go horizontally first and then vertically.
- The coordinate (-3, 1) is shown by the red circle. From 0 you go three units horizontally to the left and then 1 unit vertically upwards as shown below.
- The coordinates of P are (4, 3) and the coordinates of R are (-2, -3). The midpoint is found by taking the average of the x and y coordinates.
Average of x coordinates = \frac{4+-2}{2}=\frac{4-2}{2}=2
Average of y coordinates = \frac{3+-3}{2}=\frac{0}{2}=0
The midpoint is (2, 0).
You must follow the same process to determine the midpoint of a line even if you have negative coordinates.
Knowing how to be able to work with coordinates is an important skill that you need at both exam tiers. For the foundation paper, as long as you are able to understand the examples that have been shown within this article, then you should be able to answer most questions that you see.
For the higher paper, obviously the questions can be challenging and they can quite easily be mixed with other topics such as that of parallel and perpendicular lines. Here you need to be able to understand the use of gradients. As a recap, parallel lines have equal gradients and perpendicular lines, the gradients are the negative reciprocal of one another.
Another point to note about questions regarding coordinates is that they will generally involve the use of a diagram. Either a diagram will be provided or you should always provide yourself a diagram so that you can successfully understand the question and to be able to answer it correctly.