Transcript Document

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First, let’s take a look at….
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A little history
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A little history
• René Descartes
(1596-1650)
• philosopher
• mathematician
• joined algebra
and geometry
• credited with--Cartesian plane
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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.
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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…
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Cartesian plane
Formed by
intersecting
two
real number
lines at
right angles
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Cartesian plane
Horizontal
axis is
usually
called the
x-axis
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Cartesian plane
Vertical
axis is
usually
called the
y-axis
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Cartesian plane
Also called:
• x-y plane
• rectangular
coordinate
system
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Cartesian plane
Divides into
Four Quadrants
and…
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I
III
IV
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Cartesian plane
The intersection
of the two axes
is called the
origin
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Cartesian plane
Math Alert
The quadrants do
not include the
axes
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I
III
IV
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Cartesian plane
Math Alert
A point on the x or
y axis is not in a
quadrant
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I
III
IV
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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)
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Cartesian plane
(x,y)
The x and y of the
ordered pair,
(x,y), are called its
coordinates
(x,y)
(x,y)
(x,y)
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Cartesian plane
Math Alert
There is an infinite
amount of points
in the Cartesian
plane
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COORDINATE
PLANE
ORIGIN
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.
The point (0, 0) on a
coordinate plane, where
the x-axis and the y-axis
intersect.
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Take note of these graphing basics
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Cartesian plane
• Always start
at (0,0)---every
point “originates”
at the origin
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Cartesian plane
y
• In plotting (x,y)
---remember the
directions of
both the x and y
axis
x
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Cartesian plane
• (x,---)
x-axis goes
left and right
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Cartesian plane
• (---,y)
y-axis goes
up and down
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Now, let’s look at graphing…
(2,1)
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Cartesian plane
(2,1)
• Start at (0,0)
+
•(
, ---)
• Move right
2
(2,1)
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Cartesian plane
(2,1)
• (---, +)
• (---, 1)
• Move up 1
(2,1)
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Now, let’s look at graphing…
(4, 2)
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Cartesian plane
(4, 2)
• Start at (0,0)
• ( +, ---)
• Move right 4
(4, 2)
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Cartesian plane
(4, 2)
• (---, - )
• (---, -2)
• Move down 2
(4, 2)
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Cartesian plane
(3,5)
• Start at (0,0)
(, ---)
• Move left 3
(3,5)
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Cartesian plane
(3,5)
(3,5)
• (---, +)
• (---, 5)
• Move up 5
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Cartesian plane
(0, 4)
• Start at (0,0)
• (none,---)
• No move
right or left
(0, 4)
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Cartesian plane
(0, 4)
(0, 4)
• (0, + )
• (---, 4)
• Move up 4
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Now, let’s look at graphing…
(5,0)
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Cartesian plane
(5,0)
• Start at (0,0)
• ( ,---)
• Move left 5
(5,0)
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Cartesian plane
(5,0)
• ( ---, 0)
• No move up
or down
(5,0)
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Points in
To make it easy
Quadrant 2 have
to talk about negative x but
where on the positive y
coordinates.
coordinate plane
a point is, we
divide the
coordinate plane
into four sections
called quadrants.
Points in
Quadrant 3
have negative
x and negative
y coordinates.
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Points in
Quadrant 1
have positive x
and positive y
coordinates.
Points in
Quadrant 4
have
positive x
but
negative y
coordinates
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Cartesian plane
Directions:
Approximate
the coordinates
of the point--Or what is the
‘(x,y)’of the
point?
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(2, 4)
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(4, 2)
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(0,3)
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(3, 3)
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(1, 6)
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
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Cartesian plane
Directions:
Approximate
the coordinates
of the point
(5, 0)
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Cartesian plane
Directions:
Find the
coordinates of
the point two
units
to the left of the
y-axis and five
units above the
x-axis
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Cartesian plane
Directions:
Find the
(2,5)
coordinates of
the point two
units
to the left of the
y-axis and five
units above the
x-axis
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Cartesian plane
Directions:
Find the
coordinates of
the point on the
x-axis and three
units to the left
of the
y-axis
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Cartesian plane
Directions:
Find the
coordinates of
a point on the xaxis and three
units to the left
of the
y-axis
(3, 0)
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