Maths
Coordinates and bearing
There are many situations in which you might need to describe your position and direction of travel. For example, you may tell a friend that you will meet them on the corner, by the bus station, at 7pm, and that if they are late you will start walking up the high street. In mathematics, we use more precise ways to describe position and direction of travel.
Coordinates
The x axis is the horizontal axis.
The y axis is the vertical axis.
The origin is the point where the two axes cross - their point of intersection.
Remember that axes must always be labelled x and y.
Coordinates are written as a pair of numbers in round brackets. They are separated by a comma - for example:
(2, 3) (-1, 4) (17, 0).
The first number always refers to the x-coordinate.
The second number refers to the y-coordinate.
Now have a look at some sample exam questions:
- Question
What is the x-coordinate of the point (2, 7)?
- Answer
The x-coordinate is 2.
- Question
What is the y-coordinate of the point (3, 5)?
- Answer
The y-coordinate is 5.
We know that the first number is the x-coordinate. The x axis is horizontal, so the x-coordinate describes the horizontal position of the point.
We also know that the second number is the y-coordinate. The y axis is vertical, so the y-coordinate describes the vertical position of the point.
Example:
A is the point with coordinates (2, 1).
B is the point with coordinates (-1, -3).
- Question
Copy the grid onto squared paper.
Mark the points A (0, 3), B (3, 0), C (1, -2) and D (-2, 1).
Join A --> B --> C --> D --> A
What is the name of the quadrilateral ABCD?
- Answer
ABCD is a rectangle.
Did you get it right? If not, check that you have plotted the points correctly.
Compass directions
There are four points of the compass: north, south, east and west.
The direction halfway between north and west is described as north west. Similarly, the direction halfway between south and east is described as south east, the direction halfway between south and west is south west, and the direction halfway between north and east is north east.
Three-figure bearings
Imagine that you are in the middle of the ocean. You are lost and you cannot see any land.
You radio for help and are told to turn 125° clockwise. But 125° from where? Which direction should you be facing in the first place?
One sensible idea is to start by facing north. This is the way that 3-figure bearings work.
Always start by facing north, and always move in a clockwise direction.
Angles of less than 100° are written with a '0' in front, to make them a 3-figure bearing. For example, 060°, 021°.
Finding the bearing of A from B
Here is an example. Imagine that you are at point B. You need to travel to point A. On which bearing should you travel?
- Start by facing north.
- Move clockwise to face A.
- Measure the clockwise angle between the north line and the line AB.
- Question
Find the bearing of A from B
- Answer
Did you get 056°?
Remember to write your answer as a 3-figure bearing.
- Question
Find the bearing of A from B
- Answer
Did you get 200°?
If so - well done. You noticed that the clockwise angle had been given to you.
- Question
Find the bearing of A from B
- Answer
The correct answer is 134°.
Well done if you got it right. If not, remember that we need the clockwise angle between the north line and the line AB.
Now try a Test Bite