Plane Analytic Geometry: Two Dimension Analytic Geometry

Preface
This book is intended to serve as a reference for the contents of Plane Analytic Geometry Course taught at High School.
The content begins with the most basic definitions of the One and Two-Dimensional Cartesian Space.
Next, are presented the different types of equations that define the straight line, and the methods for conversion from one type of definition to another.
In a next chapter the different types of positioning the straight lines are analyzed, such as parallel, perpendicular, concurrent with a certain angle, etc.
In a new chapter some basic figures are analyzed such as triangles and parallelograms. Their definitions and properties as area, perimeter, are presented.
Also are analyzed the different types of equations of circumferences.
A final chapter looks at the various positions of straight lines with respect to the circumferences.
The contents contained in this book are basic for the study of Three Dimensional Analytical Geometry or Spatial Analytical Geometry, which are usually studied in other level of courses.
Нndice

Chapter 1
Basic Elements of Analytical Geometry1
Introduction
Cartesian System of One Dimension
Cartesian System of Two Dimensions
Quadrants of the Cartesian System of Two Dimensions
Problems to be Solved

Chapter 2
Straight Line Equations – General and Slope-intercept Forms
General Equation
Slope-intercept Equation
Slope-intercept equation from General Equation
General Equation from Slope-intercept equation
Slope Parameter and Linear Parameter of Slope-intercept equation
Slope-intercept Equation from two points of the straight Line
Slope-intercept Equation from Angular and Linear Coefficient
Coordinates of the Points from Slope-intercept Equation
Specific Cases of the General Equation of the Line
Problems to be Solved

Chapter 3
Straight Line Equations- Intercept-intercept and Normal and Normalized Forms
Intercept-intercept Equation of Straight Line
Obtaining the General and Slope-intercept Equation from the Intercept-intercept Equation
Normal Equation of Straight Line
Normal and Normalized Equations from General Equation of the Straight Line
General Equation from Normal Equation of Straight Line
Problems to be Solved

Chapter 4
Straight Line Equations- Parametric Equation and Trigonometric Ratio Equation
Parametric Equation
Verifications of the Parametric Equations
Trigonometric Ratio Equation
Trigonometric Ratio Equation from General Equation of Straight Line
Problems to be Solved

Chapter 5
Important Relationships between Straight Lines
Equations of Straight Lines that pass Through a Point
Straights that Pass by Two Points
Equation of the Line that passes through a Point and forms a Determined Angle with the Axis of the Abscissas
Division of a Line Segment into a Given Ratio
Distance between Two Points on a One-Dimensional System
Distance between Two Points on a Two Dimensional System
Point of Intersection of Two Straight Lines
Parallel Straight Lines
Congruent Straight Lines
Collinear Points
Problems to be Solved

Chapter 6
Important Relationships between Straight Lines
Angle between Two Straight Lines
Condition for two straight lines to be Parallels
Condition for Two Concurrent Straight Lines being Perpendicular to Each Other
Distance from a Point to a Line
Position of a Point in Relation to a Line
Bisector Line of the Angle Formed by Two Concurrent Straight Lines
Bisectors Lines of Angles of a Triangle
Problems to be Solved

Chapter 7
Circumference and Conic Curves
General Equation of Circumference
Intersection of Straight Lines and Circumferences
Conic Curves
Ellipse Equation
Hyperbola Equation
Parabola Equation
Problems to be Solved