STD IX – COORDINATE GEOMETRY – ARCHIMEDES

Cartesian system

Rene Descartes developed this system of describing the position of a point in a plane which is also known as the Cartesian system. The position of any point lying in a plane can be represented with the help of two perpendicular lines.

Dependent and Independent Variables

 In linear equation of the form: 3x + y = 5, x – 3y + 8 = 0, x = 5y – 8 etc. The letters ‘x’ and ‘y’ are called variables. If a linear equation in x and y is expressed with y as the subject of the formula (equation), y is called the dependent variable, and x is called the independent variable.

An ordered pair is the pair of two objects which occur in a particular order i.e. in which the order of object is important. (6, 8) and (8, 6) are two different ordered pairs.

Important points:

1. In an ordered pair (a, b), ‘a’ is called the first component, and b is called the second component of the ordered pair.

2. The components of ordered pairs may be the same e.g. (3, 3), (a, a), etc.

3. (a, b) and (b, a) are not the same.

4. Two ordered pairs are equal is they have the same (equal) first components and the same second component. (7, 10) = (7, 10)

GRAPHICAL SOLUTION

System of Simultaneous Linear Equation

A pair of linear equations in the same two variables form a system of simultaneous linear equation.

They are satisfied by the same pair of values of the two variables.

Two linear equations can have either only one solution, no solution or infinite solution.

DISTANCE FORMULA

Distance from different points:

X-coordinate or abscissa: The distance between a point and y-axis.

Y-coordinate or ordinate: The distance between a point and x-axis.§Form of a point on the x-axis: (x, 0); on the y-axis: (0, y)

A linear equation, ax + by + c = 0, (a, b≠zero), when represented graphically is a straight line.