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Analytic Geometry

Analytic Geometry is a branch of mathematics which deals with the principles of coordinate system with the help of algebra.

Analytic Geometry Definition:

It is a branch of algebra which helps in modeling geometric objects like - points, lines, circles etc.

Coordinate System

Introduction to Analytic Geometry:

In geometry this is the study of points, lines, curves and other geometrical shapes using algebraic methods. In this chapter we learn how to represent a point in a plane, derive the formula for finding the distance between the two points.

Ordered Pair

Two real numbers represented in the form (x, y) is called an ordered pair of real numbers.

Analytical Cartesian Coordinate System

Under Analytic Geometry we would study about Cartesian Coordinates and Cartesian Coordinate System.Every ordered pair of real numbers (x, y) is represented by a point in a plane with reference to two perpendicular lines OX and OY called the x and y axes.

Analytical Geometry1

x is called the abscissa (x is the distance from y-axis)

y is called the ordinate (y is the distance from x-axis)

This system is called the rectangular coordinate system or

the Cartesian Coordinate system.

Sign Convention Analytical Geometry Basics:

  1. x is positive for all points to the right of y axis
  2. x is negative for all points to the left of y-axis
  3. y is positive for all points above x-axis
  4. y is negative for all points below x-axis

The above sign convention leads to the partitioning of the x-y plane into four quadrants as shown under.

Analytical Geometry2

Note:

  1. y = 0 for all the points on x-axis and x = 0 for all the points on y-axis
  1. The coordinates of point of intersection of x and y-axis called the origin are (0, 0) which is usually represented by O.