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Transcript of -5 5 5 Rene Descartes hy/Personnel/susan/Webpages0506/JadeBri an/ Or the Cartesian coordinate...
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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”
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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
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Imagine the top surface of your desk stretching in every direction.
If it continued to spread , it would go right through your
neighbor . . .
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. . . and then through the classroom walls . . .
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. . . and through the school and the woods and the beach and out into space until it went on
forever in every direction.
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Then you would have a plane.
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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.
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The coordinate plane is divided by two number lines. One is
horizontal.
It has negative numbers! Where have you seen negative numbers
before?
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-5 50 10-10
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The other is vertical, with up being the positive direction and
down being the negative direction.
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-5 50 10-10
5
-5
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The coordinate plane is filled with points . . .
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. . . infinitely many points.
And somewhere among all those points is the point we call the
origin.
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The origin is the point where the
two number lines meet.
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5
-5
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The two number lines have special
names.
The horizontal number line is
called the x-axis.
x-5 50 10-10
5
-5
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The vertical number line is
called the y-axis.
y
x-5 50 10-10
5
-5
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The plural of axis is axes. We often
talk about the coordinate axes.
y
x-5 50 10-10
5
-5
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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.
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yCoordinates are always written in parentheses, with the x-value first.
yx,
x-5 50 10-10
5
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yCoordinates written in
parentheses are called an
ordered pair.
yx,
x-5 50 10-10
5
-5
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Consider the point which has coordinates,
(4, -2) -5 50 10-10
5
-5
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The first number tells you how far
to move to the side.
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5
-5
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So the 4 in (4, -2) says we need to move 4 units to
the right.
Remember to start at the origin.
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The second number tells you how far to move
up or down.
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5
-5
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The –2 in (4, -2) tells you to move down two units.
2,4
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5
-5
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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)
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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
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Give the coordinates of each point:
3,2
2,3 4,2
1,5
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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.
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Use your own words to explain what each term means:origincoordinatesquadrantaxis
ordered pair
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Get out your blue remotes!
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Where do the number lines meet?
A. QuadrantB. OriginC. AxisD. McDonald’s
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What shows the location (address) of a point?
A. OriginB. QuadrantC. AxisD. Ordered pair
http://www.gpsgazette.com/images/Harman-Kardon/GPS-500.jpg
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Which quadrant is highlighted?
A. IB. IIC. IIID. IV
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Which axis is highlighted?
A. x-axisB. y-axisC. z-axis
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5
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Now for the fun stuff…Clear your desk!