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 QUADRANTS , numbered as I , II ,III and IV ,anti clockwise from OLX so the plane consists of the axis and these quadrants.We call the plane, the CARTESIAN plane or the COORDINATE plane or the xy-plane.The axis are called the COORDINATE axes.