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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.

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.

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.