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

Two Number Lines

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 asCartesius.
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, 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

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.

Four Quadrants

When we include negative values, the x and y axes divide the space up into 4 pieces: Quadrants I, II, III and IV (They are numbered in a counterclockwise direction)

Quadrants

In Quadrant I both x and y are positive, but ...

in Quadrant II x is negative (y is still positive),

in Quadrant III both x and y are negative, and

in Quadrant IV x is positive again, while y is negative.

Like this:

Quadrant

X
(horizontal)

Y
(vertical)

Example

I

Positive

Positive

(3,2)

II

Negative

Positive

III

Negative

Negative

(-2,-1)

IV

Positive

Negative

Example: The point "A" (3,2) is 3 units along, and 2 units up.
Both x and y are positive, so that point is in "Quadrant I"
Example: The point "C" (-2,-1) is 2 units along in the negative direction, and 1 unit down (i.e. negative direction).
Both x and y are negative, so that point is in "Quadrant III" Note: The word Quadrant comes form quad meaning four. For example, four babies born at one birth are called quadruplets, a four-legged animal is aquadruped. and a quadrilateral is a four-sided polygon.

## Try this coordinate game

Practice test answers:

## Cartesian Coordinates

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

Using Cartesian Coordinates you mark a point on a graph byhow far alongandhow far upit is:(12,5)is 12 units along, and 5 units up.## X and Y Axis

left-right(horizontal) direction is commonly calledX.up-down(vertical) direction is commonly calledY.... and you are ready to go

you measure everything from there.X Axisruns horizontally through zeroY Axisruns vertically through zeroAxis: The reference line from which distances are measured.The plural of Axis is

, and is pronouncedAxesax-eez## Example:

Point

(6,4)is6 units across (in the

xdirection), and4 units up (in the

ydirection)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.

## Play With It !

Now would be a good time to play withInteractive Cartesian Coordinates

to see for yourself how it all works.

## 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.## Direction

xincreases, the point moves furtherright.When x decreases, the point moves further to the left.

yincreases, the point moves furtherup.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" (apairof numbers in a specialorder)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 upExample: (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:alongthe point isup or downthe point is## "Cartesian" ... ?

They are called

Cartesianbecause the idea was developed by the mathematician and philosopherRene Descarteswho was also known as.CartesiusHe is also famous for saying

"I think, therefore I am".## 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:to the leftdownFor example

(-6,4)means:go

backalong the x axis 6 then go up 4.And

(-6,-4)means:go

backalong the x axis 6 then godown 4.## Four Quadrants

When we include negative values, the x and y axes divide the space up into 4 pieces:Quadrants I, II, IIIandIV(They are numbered in a counterclockwise direction)In

Quadrant Iboth x and y are positive, but ...Quadrant IIx is negative (y is still positive),Quadrant IIIboth x and y are negative, andQuadrant IVx is positive again, while y is negative.Like this:

(horizontal)

(vertical)

IIINegativeIIINegativeNegativeIVNegativeExample: The point "A" (3,2) is 3 units along, and 2 units up.

Both x and y are positive, so that point is in "Quadrant I"

Example: The point "C" (-2,-1) is 2 units along in the negative direction, and 1 unit down (i.e. negative direction).

Both x and y are negative, so that point is in "Quadrant III"

Note: The word

Quadrantcomes formquadmeaningfour. For example, four babies born at one birth are calledquadruplets, a four-legged animal is aquadruped. and aquadrilateralis a four-sided polygon.## Dimensions: 1, 2, 3 and more ...

Think about this:- left-right

so any position needs justone number- left-right, and
- up-down

so any position needstwo numbers- left-right,
- up-down, and
- forward-backward,

that isthree numbers, or 3 dimensions!## 3 Dimensions

Cartesian coordinates can be used for locating points in 3 dimensions as in this example:(2, 4, 5)is shown inthree-dimensional Cartesian coordinates.

Interactive Cartesian CoordinatesHit the Coordinate GamePolar and Cartesian CoordinatesThe Number LineGraphs Index