COORDINATE GEOMETRY-NIRMAY

HISTORY

The idea of this system was developed in 1637 in writings by Descartes and independently by Pierre de Fermat, although Fermat also worked in three dimensions and did not publish the discovery. Both authors used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work.

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PIERRE DE FERMAT RENE’ DECARTES

Rene’ Decartes(1596-1950)

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INTRODUCTION

Coordinate Geometry or the system of coordinate geometry has been derived from the correspondence of the points on the number line and real number. A very unique number coordinate can be represented on a number line and any of the real number can be located on the number line. The number line represents the whole of the real number. By the way of the convection the number line is a horizontal placed line at its right hand side the positive Numbers are placed and on the left hand side the negative number are placed and they both are separated by the 0 or we can say zero is placed in the middle of them.

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COORDINATE PLANE

A two-dimensional surface on which points are plotted and located by their x and y coordinates

It has two scales, called the x-axis and y-axis, at right angles to each other. The plural of axis is 'axes' (pronounced "AXE-ease"). Points on the plane are located using two numbers - the x and y coordinates. These are the horizontal and vertical distances of the point from a specific location called the origin.

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X axisThe horizontal scale is called the x-axis. As you go to the right on the scale from zero, the values are positive and get larger. As you go to the left from zero, they get more and more negative.Y axisThe vertical scale is called the y-axis. As you go up from zero the numbers are increasing in a positive direction. As you go down from zero they get more and more negative.Axis labelingAlong each axis you will see small tic marks with numbers. These are labels to help judge the scale. They are shown every 5 units in the figure above, but can be any increment, and need not be the same on both axes.

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OriginThe point where the two axes cross (at zero on both scales) is called the origin. The origin is the point from which all distances along the x and y axes are measured. In the figure above you can drag the origin point to reposition it to a more suitable location at any time.QuadrantsThe two axes divide the plane into four areas called quadrants. The first quadrant, by convention, is the top right, and then they go around counter-clockwise. In the diagram above they are labelled Quadrant 1,2 etc. It is conventional to label them with numerals but we talk about them as "first, second, third, and fourth quadrant". They are also sometimes labelled with Roman numerals: I, II, III and IV.In the diagram above, you can drag the origin all the way into any corner and display just one quadrant at a time if you wish.

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USES OF COORDINATE GEOMETRY IN OUR DAY TO DAY

LIFE

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IN LOCATING PLACES/GEOGRAPHY

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IN MOVIE THETRES

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IN VARIOUS GRAPHS

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IN ARCHIETECTURE

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IN PREPARING BLUEPRINTS

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IN ANIMATION(especially 3D)

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THANK YOU

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