Cooridinate geometry

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Information about Cooridinate geometry

Published on May 28, 2010

Author: pnvk95


Slide 1: MATHEMATICS PROJECT Slide 2: Submitted by Akhil Govind, Anthony Lawrence, Karunya V.S, Safa Chogule Venkat Krisshna Slide 3: HISTORY OF CO-ORDINATE GEOMETRY INDEX : 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 INDEX (Continued) : INDEX (Continued) Midpoint Formula Centroid of a Triangle Bibliography Introduction to Co-ordinate Geometry : Introduction to Co-ordinate Geometry It is the foundation of most fields of geometry, including algebraic geometry, differential geometry, and discrete and computational Geometry. It is widely used in Physics and Engineering. Co-ordinate Geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. History of Coordinate Geometry : History of Coordinate Geometry Apollonius of Perga who wrote the book “On Determinate Section”. Slide 8: Omar Khayyam, who saw the relation between Geometry and Algebra. Slide 9: Rene Descartes, who developed Cartesian Geometry. Slide 10: Abraham de Moivre, who also pioneered the development of Coordinate Geometry CO-ORDINATE SYSTEM IN A PLANE : 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 by two half-axes. They are numbered from 1st to 4th and denoted by Roman numerals I(+,+) , II(-,+), III(-,-) and IV(+,-). Slide 12: Cartesian Co-ordinate System DISTANCE FORMULA : 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: Slide 14: The Distance formula is used heavily in Interior Designing Collinearity Equation : Collinearity Equation The Collinearity Equation is used in photogrammetry and remote sensing to relate coordinates in a sensor plane (in two dimensions) to object coordinates (in three dimensions). Circumcircle of a triangle : Circumcircle of a triangle A circle that passes through the vertices of a triangle is called the circumcircle of a triangle. Section Formula : Section Formula The Section Formula or ratio theorem states that , If a point p divides a directed line segment, ray AB , in the ratio m:n , then the position vector, p, of P, can be expressed in terms of A and B as: MIDPOINT FORMULA : MIDPOINT FORMULA If the coordinates of A and B are ( x1, y1) and ( x2, y2) respectively, then the midpoint, M, of AB is given by the following formula : Centroid of a Triangle : Centroid of a Triangle The Centroid of a triangle is where the three medians of the triangle intersect. Coordinates of the Centroid : Coordinates of the Centroid If the coordinates of the three vertices of a triangle are known, then the co-ordinates of Centroid are the averages of the coordinates of the vertices. BIBLIOGRAPHY : BIBLIOGRAPHY

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