Cartesian Plane 1

  • Upload
    mohde4

  • View
    224

  • Download
    0

Embed Size (px)

Citation preview

  • 8/10/2019 Cartesian Plane 1

    1/71

    End1

    Plotting Points ---

    In the Cartesian plane

    This material is the property of the AR Dept. of Education. It may be used and reproduced for non-profit, educational purposes only after contacting the ADE Distance Learning Center. mel

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    2/71

    End2

    First, lets take a look at.

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    3/71

    End3

    A little history

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    4/71

    End4

    A little history

    Ren Descartes

    (1596-1650)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    5/71

    End5

    A little history

    Ren Descartes

    (1596-1650)

    philosopher

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    6/71

    End6

    A little history

    Ren Descartes

    (1596-1650)

    philosopher

    mathematician

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    7/71End 7

    A little history

    Ren Descartes

    (1596-1650)

    philosopher

    mathematician

    joined algebra

    and geometry

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    8/71End

    8

    A little history

    Ren Descartes

    (1596-1650)

    philosopher

    mathematician

    joined algebra

    and geometry credited with---

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    9/71End

    9

    Now, lets take a look at

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    10/71End

    10

    Cartesian plane

    Formed by

    intersecting

    tworeal number

    lines at

    right angles

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    11/71End

    11

    Cartesian plane

    Horizontal

    axis is

    usually

    called thex-axis

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    12/71End

    12

    Cartesian plane

    Verticalaxis is

    usually

    called the

    y-axis

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    13/71

    End13

    Cartesian plane

    x-y plane

    Also called:

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    14/71

    End14

    Cartesian plane

    x-y plane

    rectangular

    coordinate

    system

    Also called:

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    15/71

    End15

    Now, lets take a closer look

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    16/71

    End16

    Cartesian plane

    Divides intoFour Quadrants

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    17/71

    End17

    Cartesian plane

    Divides intoFour Quadrants

    I

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    18/71

    End18

    Cartesian plane

    Divides intoFour Quadrants

    III

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    19/71

    End19

    Cartesian plane

    Divides into

    Four Quadrants

    III

    III

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    20/71

    End20

    Cartesian plane

    Divides into

    Four Quadrants

    III

    III IV

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    21/71

    End21

    Cartesian plane

    Divides intoFour Quadrants

    and

    III

    III IV

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    22/71

    End22

    Cartesian plane

    The intersection

    of the two axesis called the

    origin

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    23/71

    End23

    Cartesian plane

    Math Alert

    The quadrantsdonotinclude the

    axes

    III

    III IV

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    24/71

    End24

    Cartesian plane

    Math Alert

    A pointon the xoryaxis is notin a

    quadrant

    III

    III IV

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    25/71

    End25

    Cartesian plane

    Eachpointin the

    x-y planeis

    associated withan orderedpair,

    (x,y)

    (x,y)

    (x,y)

    (x,y)

    (x,y)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    26/71

    End26

    The xand yof theorderedpair,

    (x,y),are called itscoordinates

    Cartesian plane

    (x,y)

    (x,y)

    (x,y)

    (x,y)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    27/71

    End27

    Math Alert

    There is an infiniteamount of pointsin the Cartesian

    plane

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    28/71

    End28

    Take note of these graphing basics

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    29/71

    End29

    Always start

    at (0,0)---everypoint originates

    at the origin

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    30/71

    End30

    In plotting (x,y)

    ---remember thedirectionsofboth the xand y

    axis

    Cartesian plane

    y

    x

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    31/71

    End31

    Cartesian plane

    (x,---)

    x-axisgoes

    leftand right

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    32/71

    End32

    Cartesian plane

    (---,y)

    y-axisgoes

    upand down

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    33/71

    End33

    Now, lets look at graphing

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    34/71

    End34

    Now, lets look at graphing

    (2,1)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    35/71

    End35

    Cartesian plane

    Start at (0,0)

    ( , ---)

    Move right

    2

    (2,1)+

    (2,1)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    36/71

    End36

    Cartesian plane

    (---, )

    (---, 1)

    Move up1(2,1)

    +

    (2,1)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    37/71

    End37

    Now, lets look at graphing

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    38/71

    End38

    Now, lets look at graphing

    (4, 2)

    i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    39/71

    End39

    Cartesian plane

    Start at (0,0)

    ( , ---)

    Move right4

    +

    (4, 2)

    (4, 2)

    C i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    40/71

    End40

    Cartesian plane

    (---, )

    (---, -2) Move down 2

    (4, 2)

    -

    (4, 2)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    41/71

    End41

    Now, lets look at graphing

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    42/71

    End42

    Now, lets look at graphing

    ( 3,5)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    43/71

    C i l

  • 8/10/2019 Cartesian Plane 1

    44/71

    End44

    Cartesian plane

    (---, )

    (---, 5)

    Move up5

    +

    ( 3,5)( 3,5)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    45/71

    End45

    Now, lets look at graphing

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    46/71

    End46

    Now, lets look at graphing

    (0,4)

    C t i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    47/71

    End47

    Cartesian plane

    Start at (0,0)

    (none,---)

    Nomove

    right or left

    (0,4)

    (0,4)

    C t i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    48/71

    End48

    Cartesian plane

    (0, )

    (---, 4)

    Move up4

    + (0,4)(0,4)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    49/71

    End49

    Now, lets look at graphing

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    50/71

    End50

    Now, lets look at graphing

    ( 5,0)

    C t i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    51/71

    End51

    Cartesian plane

    Start at (0,0)

    ( ,---)

    Move left5

    ( 5,0)

    ( 5,0)

    C t i l

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    52/71

    End52

    Cartesian plane

    ( ---, 0)

    Nomove up

    or down

    ( 5,0)

    ( 5,0)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    53/71

    End53

    Now, lets look at a little

    graphing practice

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    54/71

    End54

    Cartesian plane

    Approximate

    the coordinates

    of thepoint---

    Or what is the

    (x,y)of the

    point?

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    55/71

    End55

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    (2,4)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    56/71

    End56

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    57/71

    End57

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    ( 4, 2)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    58/71

    Cartesian plane

  • 8/10/2019 Cartesian Plane 1

    59/71

    End59

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    (0,3)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    60/71

    End60

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    61/71

    End61

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    (3, 3)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    62/71

    End62

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    63/71

    End63

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    ( 1, 6)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    64/71

    End64

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    65/71

    End65

    Cartesian plane

    Approximate

    the coordinates

    of thepoint

    Directions:

    ( 5, 0)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    66/71

    End66

    Cartesian plane

    Find thecoordinates of

    thepointtwo

    unitsto the left of the

    y-axis and five

    units above thex-axis

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    67/71

    End67

    Cartesian plane

    Find thecoordinates of

    thepointtwo

    unitsto the left of the

    y-axis and five

    units above thex-axis

    Directions:

    ( 2,5)

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    68/71

    End68

    Cartesian plane

    Find the

    coordinates of

    thepointon the

    x-axis and three

    units to the left

    of the

    y-axis

    Directions:

    Cartesian plane

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    69/71

    End69

    Cartesian plane

    Find the

    coordinates of

    apointon the x-

    axis and three

    units to the left

    of the

    y-axis

    Directions:

    ( 3, 0)

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    70/71

    End70

    Plotting Points ---

    In the Cartesian plane

    This material is the property of the AR Dept. of Education. It may be used and reproduced for non-profit, educational purposes only after contacting the ADE Distance Learning Center. mel

    http://dlc.k12.ar.us/Mary/Math%20Web%20Lessons/mathlessons.htm
  • 8/10/2019 Cartesian Plane 1

    71/71