Analytic Geometry Part 1 - The Basics in Two and Three Dimensions

Analytic geometry is a branch of mathematics in which geometry is described through the use of algebra. Rene Descartes (1596-1650) is credited for conceptualizing this mathematical discipline. Recalling the basics, we can express the points of a plane as a pair of numbers with x-axis and y-axis coordinates, designated by (x, y). Note that the x-axis coordinate is termed the abscissa , and the y-axis the ordinate . 

Note that cos a and cos p are referred to as the direction cosines of the line segment described. To summarize in expanded notation  

Example Find the direction cosines and corresponding angles for a line segment AB where A is (2, -1, 4) and B is (4, 1, 2). To solve, use 

The slope m of a line segment between two points is given as  

Just store this information away for the next several chapters as we build a pre-chemometrics view of analytic geometry. 

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Analytic Geometry Part 1 - The Basics in Two and Three Dimensions... 

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