End

End 2

First, let’s take a look at….

End 3

A little history

End 4

A little history

• René Descartes (1596-1650)

• philosopher

• mathematician

• joined algebra and geometry

• credited with---

Cartesian plane

End

The year is 1630. Lying on his back, French mathematician René Descartes, watches a fly crawl across the ceiling. Suddenly, an idea comes to him. He visualizes two number lines, intersecting at a 90° angle. He realizes that he can graph the fly's location on a piece of paper. Descartes called the main horizontal line the x-axis and the main vertical line the y-axis. He named the point where they intersect the origin.

End

Descartes represented the fly's location as an ordered pair of numbers.

The first number, the x-value, is the horizontal distance along the x-axis, measured from the origin.

The second number, the y-value, is the vertical distance along the y-axis, also measured from the origin.

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Now, let’s take a look at…

End 8

Cartesian plane

Formed by

intersecting

two

real number

lines at

right angles

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Cartesian plane

Horizontal axis isusually

called thex-axis

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Cartesian plane

Verticalaxis isusually

called they-axis

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Cartesian plane

• x-y plane

• rectangular

coordinate

system

Also called:

End 12

Cartesian plane

Divides intoFour Quadrants

and…

III

III IV

End 13

Cartesian plane

The intersection

of the two axes is called the

origin

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Cartesian plane

Math AlertThe quadrants do not

include the axes

III

III IV

End 15

Cartesian plane

Math AlertA point on the x or y

axis is not in a quadrant

III

III IV

End 16

Cartesian plane

Each point in the

x-y plane is associated with an ordered pair,

(x,y)

(x,y)

(x,y)

(x,y)

(x,y)

End 17

The x and y of the ordered pair,

(x,y), are called its coordinates

Cartesian plane

(x,y)

(x,y)

(x,y)

(x,y)

End 18

Math AlertThere is an infinite

amount of points in the Cartesian

plane

Cartesian plane

End

The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers.

COORDINATE PLANE

The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.

ORIGIN

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Take note of these graphing basics

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• Always start

at (0,0)---every

point “originates” at the origin

Cartesian plane

End 22

• In plotting (x,y)---remember the

directions of both the x and y

axis

Cartesian planey

x

End 23

Cartesian plane

• (x,---)

x-axis goes

left and right

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Cartesian plane

• (---,y)

y-axis goes

up and down

End 25

Now, let’s look at graphing…

(2,1)

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Cartesian plane

• Start at (0,0)

• ( , ---)

• Move right 2

(2,1)+

(2,1)

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Cartesian plane

• (---, )

• (---, 1)

• Move up 1(2,1)

+

(2,1)

End 28

Now, let’s look at graphing…

(4, 2)

End 29

Cartesian plane

• Start at (0,0)

• ( , ---)

• Move right 4

+

(4, 2)

(4, 2)

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Cartesian plane

• (---, )

• (---, -2)

• Move down 2

(4, 2)

-

(4, 2)

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Cartesian plane

• Start at (0,0)

( , ---)

• Move left 3

( 3,5)-

( 3,5)

End 32

Cartesian plane

• (---, )

• (---, 5)

• Move up 5

+

( 3,5)( 3,5)

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Cartesian plane

• Start at (0,0)

• (none,---)

• No move right or left

(0,4)

(0,4)

End 34

Cartesian plane

• (0, )

• (---, 4)

• Move up 4

+ (0,4)(0,4)

End 35

Now, let’s look at graphing…

( 5,0)

End 36

Cartesian plane

• Start at (0,0)

• ( ,---)

• Move left 5

( 5,0)

( 5,0)

End 37

Cartesian plane

• ( ---, 0)

• No move up

or down

( 5,0)

( 5,0)

End

To make it easy to talk about where on the coordinate plane a point is, we divide the coordinate plane into four sections called quadrants.

Points in Quadrant 1

have positive x and positive y coordinates.

Points in Quadrant 2 have negative x but positive y coordinates.

Points in Quadrant 3 have negative x and negative y coordinates.

Points in Quadrant 4

have positive x

but negative y

coordinates.

End

End 40

Cartesian plane

Approximate

the coordinates

of the point---

Or what is the

‘(x,y)’of the

point?

Directions:

End 41

Cartesian plane

Approximate

the coordinates

of the point

Directions:

(2,4)

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Cartesian plane

Approximate

the coordinates

of the point

Directions:

End 43

Cartesian plane

Approximate

the coordinates

of the point

Directions:

( 4, 2)

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Cartesian plane

Approximate

the coordinates

of the point

Directions:

End 45

Cartesian plane

Approximate

the coordinates

of the point

Directions:

(0,3)

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Cartesian plane

Approximate

the coordinates

of the point

Directions:

End 47

Cartesian plane

Approximate

the coordinates

of the point

Directions:

(3, 3)

End 48

Cartesian plane

Approximate

the coordinates

of the point

Directions:

End 49

Cartesian plane

Approximate

the coordinates

of the point

Directions:

( 1,6)

End 50

Cartesian plane

Approximate

the coordinates

of the point

Directions:

End 51

Cartesian plane

Approximate

the coordinates

of the point

Directions:

( 5,0)

End 52

Cartesian plane

Find the coordinates of the point two

unitsto the left of they-axis and five units above the

x-axis

Directions:

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Cartesian plane

Find the coordinates of the point two

unitsto the left of they-axis and five units above the

x-axis

Directions:

( 2,5)

End 54

Cartesian plane

Find the

coordinates of

the point on the x-axis and three units to the left

of the

y-axis

Directions:

End 55

Cartesian plane

Find the

coordinates of

a point on the x-axis and three units to the left

of the

y-axis

Directions:

( 3,0)

End 56