Final Cover - For Printing

ANALYTICAL GEOMETRY

Analytical Geometry
Analytical Geometry is a branch of mathematics in which the algebraic methods are used to
study the geometrical concepts. De Cartes (1596-1650), a French mathematician invented
this idea and hence analytical geometry is called as Cartesian Geometry, named after the
inventor, who is considered as the father of analytical geometry.

1. Angle of inclination
   If a line makes an angle θ with the positive direction of the x-axis, then^ θ is called
   the angle of inclination.

The idea needs verbal explanation along with the provision of an embossed diagram

depicting the angle of inclination formed.

2. Slope of a line
   The tangent of the angle of inclination, that is tan^ θ is called the slope of the line
   or the gradient of the line. The slope of the line is denoted by m. That is slope =
   m=tan θ

Note:

1. The angle θ is measured from the positive direction of the x-axis towards the line
   in the anti-clockwise direction.


2. The slope of any line parallel to x-axis is zero since tan 0^0 = 0.


3. The slope of any line perpendicular to x-axis is infinity since tan90^0 = undefined.


4. If the angle θ is acute, then the slope tan θ is positive.


5. If the angle θ is obtuse, then the slope tan θ is negative.

Module 82