Describe positions in the four quadrants | Year 6 Mathematics PDF Download

What is a Coordinate?

• It is possible to position a point on a grid using a pair of numbers or coordinates.
• A pair of coordinates is an example of an ordered pair since the order of the two numbers is important!
• Which number gets written first and which number gets written second matters.
• For example, a point with the coordinates (2, 3) is in a different place from a point with the coordinates (3, 2).
• The grid below shows a pair of axes, dividing the grid into four parts, or quadrants.
  

What are quadrants?

• The x-axis is the horizontal axis. In this example, the x-axis is numbered from -3 to 3.
• The y-axis is the vertical axis. In this example, the y-axis is also numbered from -3 to 3.
• The two axes intersect at right angles at the point we call the origin – or the place we start from when positioning a point with given coordinates.
• The letter P positions a point with coordinates (2, 3). This point is located in the first quadrant.
• The letter Q positions a point with coordinates (3, 2). This point is also located in the first quadrant.
  
• The four quadrants are labeled as follows – the First Quadrant, the Second Quadrant, the Third Quadrant, and finally the Fourth Quadrant.
• Only in the first quadrant will both the x and y coordinates be positive.
• Negative coordinates will be introduced to positive points in the other three quadrants.

Examples

Example 1:

The diagram above shows an isosceles triangle, LMN.
The co-ordinates of the vertices of the triangle are: L(4,5), M(4,1) and N(-4,3).
If the triangle is reflected in the x axis then the co-ordinates of the reflected image would be L¹(4,-5), M¹(4,-1) and N¹(-4,-3).
So, when reflected in the x axis, we have:
L (4,5) → L¹ (4,-5)
M (4,1) → M¹ (4,-1)
N (-4,3) → N¹ (-4,-3)
Look at what happens to the x and y co-ordinates when points are reflected in the x axis.
The x co-ordinate stays the same, whereas the y co-ordinate 'changes sign’, i.e. if it was positive it now becomes negative and if it was negative it changes to positive!
We could generalise and say:
A (x,y) → A¹ (x, -y)

Example 2:

The point A is positioned in the first quadrant.
The co-ordinates of A are (1,3)
We can just write this as A(1,3)
The point B is positioned in the second quadrant.
The co-ordinates of B are (-3,3)
We can just write this as B(-3,3)
The point C is positioned in the third quadrant.
The co-ordinates of C are (-3,-2)
We can just write this as C(-3,-2)
The point D is positioned in the fourth quadrant.
The co-ordinates of D are (1,-2)
We can just write this as D(1,-2)
The four points could be joined, A to B, B to C, C to D and finally D to A to form the rectangle ABCD.