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# Introduction to Analytical Geometry

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 Sub Topics The concept of Analytical Geometry was given by Mr. Percey F. Smith and Mr. Arthur Sullivan Gale. Mr. Percey F. Smith was a professor of mathematics in Sheffield scientific school, Yale University and Arthur Sullivan Gale was an assistant professor of mathematics in the University of Rochester. Now, we will see introduction to analytical geometry. Analytic geometry and Algebra both are similar, they are used to design the geometric objects in the mathematics, and these geometric objects are points, straight line, and Circle etc. In the plane of geometry the points are represented as Ordered Pair and in case of Straight Line it is represented as Set of points which satisfy the linear equation and the analytic geometry which satisfies linear equation are known as linear algebra. There are some different names for analytic geometry like Cartesian geometry is also known as analytic geometry. This plane analytic geometry is based on the coordinate system and the principal of algebra and analysis. Now, we will see how to find the distance and angle in analytic geometry. Suppose we have coordinates m1, m2 and n1, n2 for the plane of geometry: Then we will see how to find the distance of plane of analytic geometry by using above coordinates: d = √ (m2 - m1)2 + (n2 - n1)2; Where ‘d’ is distance of analytic geometry. We use pythagoras theorem for finding the distance of analytic geometry; Now we will find the angle of plane of geometry: The angle of geometry is: ∅ = arctan (p); Where ‘p’ is the Slope of line; Using this formula we can find the distance of plane of analytic geometric. This is all about analytical geometry introduction.

## Define Inclination of a Line

A line can be plotted on a graph, and when we plot any line of the graph, it is inclined at certain angle in a coordinate plane. This plotting of the line on the Cartesian plane and the angle formed by the line on the axis is called inclination of the line and is represented by the angle Ө. Here, we define Inclination of a Line. By the term Inclination of a line, we Mean how much a line is inclined on a particular axis.
The inclination of an angle helps us to find the Slope of any line which is represented by tan Ө. By the angle of inclination we mean the measure of angle Ө, that the line or the part of the line forms with the positive direction of the x – axis and it is measured in anti clock wise direction. So, we say that the value of Ө is always a positive quantity. Thus, it is clear that the value of Ө is always between 0 degrees to 180 degrees.
We must look at the following observations about the Slope or inclination of the line:
1. The inclination of the line which is parallel to x – axis, or the x – axis itself is always 0 degrees and 180 degrees.
2. The inclination of the line which is parallel to y – axis or y – axis itself is 90 degrees.
Thus we come to the conclusion that any line parallel to the x axis or the x axis itself is called a horizontal line and the line which is parallel to y axis, or the y- axis itself is called the perpendicular of the vertical line. Another type of line is oblique line, which we say is neither a parallel line nor a horizontal line. If we know the inclination of any given line then we can easily find the slope of that line.