COORDINATE GEOMETRY

COORDINATE GEOMETRY

1. A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

   •  René Descartes,  the great French mathematician of the 7th century, liked to lie in bed and think ! One day,when resting in bed , he solved  a problem of describing the position of a point in a plane . His method was a development of older idea of latitude and longitude.  In honor of Descartes,  the system used for describing the position of a point in a plane is also known as CARTESIAN System.
   • CARTESIAN SYSTEM
     • Here , we take two number lines, calling them X'X and Y'Y . Place X'X horizontal and write the numbers on it just as written on a number line .We do the same thing with Y'Y , except that Y'Y is kept vertical, not horizontal .
       • The x- coordinates are  known  as ABSCISSA and the  y- coordinates are  called the ORDINATE .
       • Now,we combine both the lines in such a way that the two lines cross each other at their zeros or origins. The horizontal line X'X is called x-axis and the vertical line Y'Y is called y-axis.
       • The points where X'X and Y'Y cross is called ORIGIN,and is denoted by O. Since the positive numbers lie on the directions OX and OY,they are called the positive directions . Similarly, OX' and OY' are called the negative directions.
         • We observe that the axes divide the plane into 4 parts . These four parts are called the quadrants (one fourth part) ,numbered as I,II,III and IV anticlockwise from OX .So the plane consists of the axes and the quadrants .We call such plane,the CARTESIAN PLANE or COORDINATE PLANE , or the xy-plane . The axes are called theCOORDINATE AXES