2,4

5,1

-5

-5

5

5

2,2 1,7

Rene Descartes

http://www.gla.ac.uk/departments/philosophy/Personnel/susan/Webpages0506/JadeBrian/descartes.jpg

Or the “Cartesian coordinate system”

Objectives

• Identify numbers that are less than zero by extending the number line.

• Identify components of the Cartesian plane, including the x-axis, y-axis, origin, and quadrants.

-5 50 10-10

Imagine the top surface of your desk stretching in every direction.

If it continued to spread , it would go right through your

neighbor . . .

. . . and then through the classroom walls . . .

. . . and through the school and the woods and the beach and out into space until it went on

forever in every direction.

Then you would have a plane.

In mathematics, a plane is a flat surface that goes on forever in

every direction.

In math, we have been using only one quadrant of the coordinate plane to plot

points.

The coordinate plane is divided by two number lines. One is

horizontal.

It has negative numbers! Where have you seen negative numbers

before?

-5 50 10-10

-5 50 10-10

The other is vertical, with up being the positive direction and

down being the negative direction.

-5 50 10-10

5

-5

The coordinate plane is filled with points . . .

. . . infinitely many points.

And somewhere among all those points is the point we call the

origin.

The origin is the point where the

two number lines meet.

-5 50 10-10

5

-5

The two number lines have special

names.

The horizontal number line is

called the x-axis.

x-5 50 10-10

5

-5

The vertical number line is

called the y-axis.

y

x-5 50 10-10

5

-5

The plural of axis is axes. We often

talk about the coordinate axes.

y

x-5 50 10-10

5

-5

To study a point, we need to know where to find it. So we give it

coordinates. We learned about these last week.

(2, 3)

Coordinates are like an address. They tell you how you can get to a point if you start at the origin.

yCoordinates are always written in parentheses, with the x-value first.

yx,

x-5 50 10-10

5

-5

yCoordinates written in

parentheses are called an

ordered pair.

yx,

x-5 50 10-10

5

-5

Consider the point which has coordinates,

(4, -2) -5 50 10-10

5

-5

The first number tells you how far

to move to the side.

-5 50 10-10

5

-5

So the 4 in (4, -2) says we need to move 4 units to

the right.

Remember to start at the origin.

-5 50 10-10

5

-5

The second number tells you how far to move

up or down.

-5 50 10-10

5

-5

The –2 in (4, -2) tells you to move down two units.

2,4

-5 50 10-10

5

-5

To get to the origin from the origin, we don’t

move at all.

0,0

So the origin is designated by the ordered pair,

(0, 0)

-5 50 10-10

5

-5

The two number lines divide the plane into four

regions.

Quadrants are labeled with

Roman Numerals.

We call the regions

quadrants.

In Quadrant I, all numbers are

positive.

In Quadrant II, x-values are negative, while y-values are

positive.

In Quadrant III, x- and y-values are both negative.

In Quadrant IV, x-values are positive and y-values are

negative.

III

III IV-5 50 10-10

5

-5

Give the coordinates of each point:

3,2

2,3 4,2

1,5

Tell how you can find each point:

0,4

Remember to start at the origin!

7,8

5,4 9,0 12,7

From the origin, move to the right 8 units, then down 7 units.

Use your own words to explain what each term means:origincoordinatesquadrantaxis

ordered pair

Get out your blue remotes!

Where do the number lines meet?

A. QuadrantB. OriginC. AxisD. McDonald’s

-5 50 10-10

5

-5

What shows the location (address) of a point?

A. OriginB. QuadrantC. AxisD. Ordered pair

http://www.gpsgazette.com/images/Harman-Kardon/GPS-500.jpg

Which quadrant is highlighted?

A. IB. IIC. IIID. IV

-5 50 10-10

5

-5

Which axis is highlighted?

A. x-axisB. y-axisC. z-axis

-5 50 10-10

5

-5

Now for the fun stuff…Clear your desk!