coordinate geometry

coordinate geometry

1. cartesian plain

   • A Cartesian plane is defined by two perpendicular number lines, X and Y. It extends to infinity in both directions. It has a centre usually denoted by O.
   • horizontal
     • The horizontal line is called X-axis while the vertical line is called Y-axis.
     • Cartesian System.
       • The system which we have described to label points in a plane is also known as the Cartesian System.
       • origin
         • The intersection point of the axes is the zero of the Cartesian System. This point will generally be denoted by O (also known as origin).
         • coordinates
           • The pair of real numbers x and y which uniquely determine the position of a point P in the plane are referred to collectively as the coordinates of P.
           • abscissa
             • The first real number (in this case, x) tells us the distance we will have to cover along X to reach P. We will refer to this real number as the x-coordinate or abscissa of P.
             • ordinate
               • The second real number (in this case, y) tells us the distance we will have to cover parallel to Y to reach P. We will refer to this real number as the y-coordinate or ordinate of P.
               • quadrants.
                 • The two axes (X and Y) divide the cartesian plane into four regions, or quadrants.