1. Cartesian Co-ordinates
Working with Ordered Pairs

2. Cartesian Coordinates
Cartesian coordinates can be used to pinpoint where you are on a map or graph.

3. Using Cartesian Coordinates you mark a point on a graph by how far along and how far up it is:
The point (12,5) is 12 units along, and 5 units up.

4. X and Y Axis
The left-right (horizontal) direction is commonly called X.
The up-down (vertical) direction is commonly called Y.
Put them together on a graph ...
... and you are ready to go!

5. Where they cross over is the "0" point, you measure everything from there.
The X Axis runs horizontally through zero
The Y Axis runs vertically through zero
Axis: The reference line from which distances are measured.
The plural of Axis is Axes, and is pronounced ax-eez
And you can remember which is which by:
x is A CROSS, so x is ACROSS the page.

6. Example: Point (6,4) is 6 units along (in the x direction), and
4 units up (in the y direction)
So (6,4) means:
Go along 6 and then go up 4 then "plot the dot".

7. Like 2 Number Lines Put Together
It is like we put two Number Lines together, one going left-right, and the other going up-down.

8. Writing Coordinates
The coordinates are always written in a certain order: the horizontal distance first, then the vertical distance.
This is called an "ordered pair" (a pair of numbers in a special order)
And usually the numbers are separated by a comma, and parentheses are put around the whole thing like this: (3,2)
Example: (3,2) means 3 units to the right, and 2 units up
Example: (0,5) means 0 units to the right, and 5 units up.

9. The Origin
The point (0,0) is given the special name "The Origin", and is sometimes given the letter "O".

10. "Cartesian" ... ?
They are called Cartesian because the idea was developed by the mathematician and philosopher Rene Descartes who was also known as Cartesius.
He is also famous for saying "I think, therefore I am".

11. What About Negative Values of X and Y?
Just like with the Number Line, you can also have negative values.
Negative: start at zero and head in the opposite direction:
Negative x goes to the left
Negative y goes down

12. So, for a negative number:
go backwards for x
go down for y
For example (-6,4) means: go back along the x axis 6 then go up 4.
And (-6,-4) means: go back along the x axis 6 then go down 4.