Introduction:
Geometry is one of the most ancient branches of mathematics. The Greeks systematically studied it about four centuries B.C. Most of the geometry taught in schools is due to Euclid who expounded thirteen books on the subject (300 B.C.). A French philosopher and mathematician Rene Descartes (1596 - 1650 A.D.) introduced algebraic methods in geometry which gave birth to analytical geometry (or coordinate geometry).
Coordinate System:
The ordered pair (x , y) gives us enough information to locate the point P. Thus, with every point P in the plane, we can associate an ordered pair of real numbers (x , y) and we say that P has coordinates (x , y). It may be noted that x and y are the directed distances of P from the y-axis and the x-axis respectively. The reverse of this technique also provides a method for associating exactly one point in the plane with any ordered pair (x , y) of real numbers. This method of pairing off in a one-to-one fashion, the points in a plane with ordered pairs of real numbers is called the two dimensional rectangular (or Cartesian) coordinate system.
x-coordinate and y-coordinate:
If (x , y) are the coordinates of a point P, then the first member (component) of the ordered pair is called the x-coordinate or abscissa of P and the second member of the ordered pair is called the y-coordinate or ordinate of P.
Important Notes:
Note that abscissa is the always first element and the ordinate is second element in an ordered pair.
Geometry is one of the most ancient branches of mathematics. The Greeks systematically studied it about four centuries B.C. Most of the geometry taught in schools is due to Euclid who expounded thirteen books on the subject (300 B.C.). A French philosopher and mathematician Rene Descartes (1596 - 1650 A.D.) introduced algebraic methods in geometry which gave birth to analytical geometry (or coordinate geometry).
Coordinate System:
The ordered pair (x , y) gives us enough information to locate the point P. Thus, with every point P in the plane, we can associate an ordered pair of real numbers (x , y) and we say that P has coordinates (x , y). It may be noted that x and y are the directed distances of P from the y-axis and the x-axis respectively. The reverse of this technique also provides a method for associating exactly one point in the plane with any ordered pair (x , y) of real numbers. This method of pairing off in a one-to-one fashion, the points in a plane with ordered pairs of real numbers is called the two dimensional rectangular (or Cartesian) coordinate system.
x-coordinate and y-coordinate:
If (x , y) are the coordinates of a point P, then the first member (component) of the ordered pair is called the x-coordinate or abscissa of P and the second member of the ordered pair is called the y-coordinate or ordinate of P.
Important Notes:
Note that abscissa is the always first element and the ordinate is second element in an ordered pair.
Comments
Post a Comment