rizal park, manila
TRANSCRIPT
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Rizal Park, Manila
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New York City, USA
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Eiffel Tower Paris
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Singapore Merlion
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The Basilica of Saint Peter - Rome
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LOCATE EACH OF THESE PLACES ON THE MAP
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ManilaNew York
Singapore
Paris France
Rome, Italy
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NOTE:
A place on the map isdescribed according to latitudeand longitude. Illustrate how aplace on the map can be locatedusing the latitude and longitude,and vice versa.
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CARTESIAN COORDINATE
PLANE
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René Descartes, 1596 - 1650
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René Descartes• Cartesian mathematics was invented by (and
is named after) French philosopher, physiologist, and mathematician René Descartes, 1596 - 1650.
• Descartes is famous not just for inventing Cartesian mathematics, which at the time was a stunning unification of algebra and geometry. He is also well-known for making a pretty good stab of answering the question “How do I know something is true?”, a question that has kept generations of philosophers happily employed.
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Points and their Coordinates
y axis
x axis
origin
y axis – the verticalline or the axis ofthe ordinates.
x axis – horizontalline or the axis ofthe abscissa.
Origin – theintersection of theaxes.
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The Cartesian Plane is divided into four quadrants.
III
III IV
(+,+)(-,+)
(-,-) (+,-)
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Plotting Points in the Cartesian Plane
5
4
(5, 4) is an example ofan ordered pair
xcoordinate
y coordinate
( 5 , 4 )
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Plotting Points in the Cartesian Plane
(5, 4) is an example ofan ordered pair ( 5 , 4 )
Quadrant I
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Example 1: It is like entering a hotel. Plot (-3,4)
(x
in the door
Up the elevator
(– 3,
left 3up 4
, y)
4)
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Plot ( -3, 4)
(-3 , 4)
Quadrant II
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Example 2. Identify the coordinates of points C, D, E and F. In which quadrant is each point located?
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Example 2. Identify the coordinates of points C, D, E and F. In which quadrant is each point located?
(x, y) - Quadrant
C (4,5) - QI
D (3,-5) - QIV
E (-5,2) - QII
F (-3,-3) - QIII
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Try This!
Identify thecoordinatesof points L,N and O.In whichquadrant iseach pointlocated?
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Example 3.Plot the following points.
E(5, 0) F(0, 6)
G(– 4, 0) H(0, – 3)
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F(0, 6)
G(– 4, 0)
H(0, – 3)
E(5, 0)
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What do you notice about their coordinates?
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All points lie on the axes, not in quadrants
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The Cartesian Plane is divided into four axes.
Along positive y axis
Along positive x axis
Along negative y axis
Along negative x axis
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Activity
In what quadrant or axis is each point located
1.(-2 , -2)2.(4, -6)3.(0 , 5)4.( 5, 8)5.( -4, 5)
6. ( 4, 0)7. (.5 , 0)8. (3 , 4)9. ( 4, 7)10. (- 2.5, 6)
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Part II. Write a generalization
1. In which quadrant do points lie if both their
abscissa and ordinate is positive?
2. In which quadrant do points lie if their abscissa
is zero?
3. In which quadrant do points lie if both their
ordinate is a negative real number?
4. In which quadrant do points lie if both their
abscissa and ordinate is negative?
5. n which quadrant do points lie if their ordinate is
zero?
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THANK YOU