Co ordinate geometry

 

Cartesian Coordinates

Using Cartesian Coordinates we 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.

 

They are also called Rectangular Coordinates because it is like we are forming a rectangle.

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 we are ready to go
Where they cross over is the "0" point, we 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

 

Example:

Point (6,4) is

6 units across (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".

And you can remember which axis is which by:

x is A CROSS, so x is ACROSS the page

Like 2 Number Lines Put Together

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

Direction

	As x increases, the point moves further right. When x decreases, the point moves further to the left.
	As y increases, the point moves further up. When y decreases, the point moves further down.

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.

In other words, only 5 units up.

The Origin

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

Abscissa and Ordinate

You may hear the words "Abscissa" and "Ordinate" ... they are just the x and y values:

• Abscissa: the horizontal ("x") value in a pair of coordinates: how far along the point is
• Ordinate: the vertical ("y") value in a pair of coordinates: how far up or down the point is

"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".

What About Negative Values of X and Y?

Just like with the Number Line, we 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

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.