Analytic Geometry
 

 

 

Contents

 

Analytic Geometry

 

Basic Concepts

2

Area of Polygon

 

Equation of Straight Line

 

Parallel Lines

 

Perpendicular Lines

 

Examples

 

Quiz

 

Geometry Main Page 

Basic Concepts
 
 
Distance between two points
 
 
To find the distance between two points A and B, by Pythagoras Theorem,
                                                       
 
Note: It does not matter whether you use x1 - x2 or x2 - x1 (same for y-values). Since this value is squared, the final results are the same.
 
Midpoint of two points
 
 
C is the midpoint of the segment AB.
--> AC = BC
--> AK = KL    (projection of AB onto AL)
--> x1 - x = x - x2
-->
   
 
Similarly, y is worked out to be
    
 
Hence, the coordinates of the midpoint C are
                       
 
For the following quadrilaterals, their diagonals intersect at their midpoints : parallelogram, square, rectangle and rhombus.