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INDEX
Introduction to Co-ordinate Geometry
History of Co-ordinate Geometry
Co-ordinate System in a Plane
Distance Formula
Collinearity of Two Points
Circumcircle of a Triangle Section Formula
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INDEX (Continued)
Midpoint Formula
Centroid of a Triangle
Bibliography
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Introduction to Co-ordinate
Geometry
Co-ordinate Geometry, is the study of
geometry using a coordinate system
and the principles of algebra andanalysis.
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History of Coordinate
Geometry
Apollonius of
Perga who wrote
the book OnDeterminate
Section.
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Omar Khayyam,who saw the
relation between
Geometry andAlgebra.
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Rene Descartes,who developed
Cartesian
Geometry.
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Abraham deMoivre, who also
pioneered the
development ofCoordinate
Geometry
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CO-ORDINATE SYSTEM IN A
PLANE
The axes of a two-dimensional Cartesian
system divide the plane into four infinite
regions, called quadrants, each bounded bytwo half-axes. They are numbered from 1st to
4th and denoted by Roman numerals I(+,+) ,
II(-,+), III(-,-) and IV(+,-).
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Cartesian Co ordinate System
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DISTANCE FORMULA
The formula is derived from the Pythagoreas
Theorem. It is used by engineers in Interior
designing
It states that-
Given the two points (x1, y1)
and (x2, y2), the distance between these
points is given by the formula:
d =
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The Distance formula is used heavily in
Interior Designing
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Collinearity Equation
The Collinearity Equation is used in photogrammetryand remote sensing to relate coordinates in a sensor
plane (in two dimensions) to object coordinates (in
three dimensions).
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Circumcircle of a triangle
A circle that passes through thevertices of a triangle is called the
circumcircle of a triangle.
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Section Formula
The Section Formula or ratio theorem states that ,
If a point p divides a directed line segment, rayAB , in the ratio m:n , then the position vector,p, of P, can be expressed in terms of A and B
as:
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MIDPOINT FORMULA
If the coordinates of A and B are ( x1, y1) and ( x2,
y2) respectively, then the midpoint, M, of AB is givenby the following formula :
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entroid of a Triangle
The Centroid of a triangle is wherethe three medians of the triangle
intersect.
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Coordinates of the Centroid
If the coordinates of the threevertices of a triangle are known, then
the co-ordinates of Centroid are theaverages of the coordinates of the
vertices.
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BIBLIOGRAPHY
www.wikipedia.org
www.images.google.com
www.google.comwww.wolframalpha.com