Coordinate Geometry

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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

Coordinate Geometry

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