The document discusses the Cartesian coordinate system, created by mathematician René Descartes, which combines algebra and geometry to describe the position of points in a plane. It details how to plot points using ordered pairs on the x and y axes, explains the significance of the origin, quadrants, and coordinates, and highlights the importance of graphic representations for data visualization. Additionally, it covers various types of frequency distributions used in organizing raw data.

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Cartesian
Coordinate
K.THIYAGU
Assistant Professor
Department of Education
Central University of
Kerala, Kasaragod

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Abscissa Ordinate Cartesian Quadrants Graph
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Rene Descartes
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The Cartesian Coordinate Plane
The Cartesian
plane was the
brainchild of
French
mathematician
Rene Descartes
trying to combine
algebra and
geometry
together.

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A very famous mathematician called Rene Descartes lay in bed one night. As he lay there, he looked up at the ceiling in
his bedroom. He noticed a fly was asleep on the ceiling. Descartes, being a mathematician wondered if he could figure out
a way of stating where exactly the fly was on the ceiling. Obviously it has to be a precise description he thought. I can’t
really say, “To the left” or “Near the right “or “In the middle”.
Coordinate Geometry: Get to the point!
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Descartes decided that if he drew two lines at right angles to each other, then he might be able to
come up with a way of describing the exact position of the fly.
How do you think this would have helped him?
When Descartes looked up at his ceiling, this is what he saw. A fly resting there.
He began to think about how he might be able to describe the exact position of the fly.
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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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Coordinates
X
X’
Y
Y’
O
Origin
1 2 3 4
+ve direction
-1
-2
-3
-4
-ve direction
-1
-2
-3
-ve
direction
1
2
3
+ve
direction
X-axis : X’OX
Y-axis : Y’OY
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Coordinates
X
X’
Y
Y’
O
1 2 3 4
-1
-2
-3
-4
-1
-2
-3
1
2
3
(2,1)
(-3,-2)
Ordinate
Abscissa
(?,?)
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Coordinates
X
X’
Y
Y’
O
1 2 3 4
-1
-2
-3
-4
-1
-2
-3
1
2
3
(2,1)
(-3,-2)
Ordinate
Abscissa
(4,?)
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Coordinates
X
X’
Y
Y’
O
1 2 3 4
-1
-2
-3
-4
-1
-2
-3
1
2
3
(2,1)
(-3,-2)
Ordinate
Abscissa
(4, 2.5)
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Quadrants
X
X’ O
Y
Y
’
I
II
III IV
(+,+)
(-,+)
(-,-) (+,-)
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Quadrants
X
X’ O
Y
Y’
I
II
III IV
(+,+)
(-,+)
(-,-) (+,-)
Q : (1,0) lies in which Quadrant?
Ist? IInd?
A : None. Points which lie on the axes do not lie in any quadrant.
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Each coordinate plane is divided
into quadrants. Using the “ordered
pairs” or the x- and y-axes you can
find a point on the plane.
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To plot an ordered pair,
begin at the origin, the
point (0, 0), which is
the intersection of the
x-axis and y-axis.
The first coordinate tells
how many units to move
left or right; the second
coordinate tells how
many units to move up
and down.
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x-axis – the horizontal axis on a coordinate plane.
y-axis – the vertical axis on a coordinate plane.
x-coordinate – the first number in an ordered pair; it tells the units to
move right or left from the origin.
y-coordinate – the second number in an ordered pair; it tells the units
to move up or down from the origin.
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Order pairs – a pair of numbers used to locate a point on a coordinate plane.
Coordinate plane – a plane formed by the intersection of a horizontal number
line called the x-axis and a vertical line called the y-axis.
Origin – the point where the x-axis and the y-axis intersect on the coordinate
plane.
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Draw this coordinate plane on
graph paper and label all parts.
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Co-ordinate Axes
The two lines XOX’ and YOY’ which intersect
each other at right angles and at a point O.
Both the axes should be appropriately labeled
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Abscissa
• Abscissa is the X-axis
• XOX’ line
• It is horizontal line
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Ordinate
•Y-axis
•YOY’ line
•Ordinate is the vertical line
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Origin • The point of origin or the zero point
• point of intersection of XOX’ AND YOY’.
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Quadrants X-axis Y - axis
I + +
II - +
III - -
IV + -
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Graph Diagram
Graphs are constructed on graph paper Diagrams can be generated and constructed on plane paper.
Graphs are used by statisticians for research work Diagrams are used for publicity
Graphs are bounded by two axies Diagrams are not bounded by the two axis
Graphs have not many dimensions depending on choices Diagrams have many dimensions depending on choices.
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Significance of Graphic Presentation
• It gives a bird’s eye view of the entire data. An old saying ‘ A picture is worth 10000 words’ is very true
• The impression on graphs last much longer than figures in a tabular form.
• Graphic presentation looks attractive and fascinating
• It has a delight to the eye and a better visual impact
• It never gives strain to one’s mind
• The basic features of data can be understood
• Data are grasped through graph; at a glance it is understood.
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Raw Data: Data collected in original form.
Frequency: The number of times a certain value or class of values occurs.
Frequency Distribution (Table): The organization of raw data in table form with classes and frequencies.
Categorical Frequency Distribution: A frequency distribution in which the data is only nominal or ordinal.
Ungrouped Frequency Distribution: A frequency distribution of numerical data. The raw data is not grouped.
Grouped Frequency Distribution: A frequency distribution where several numbers are grouped into one class.
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Thank You