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WORKBOOK
ANALYTIC GEOMETRY
NUMBER LINE
On the number line, each point is represented by a coordinate (number)
The Ruler Postulate: The points of a line can be placed in a correspondence with the real numbers
such that
A. for every point of the line there corresponds exactly one real number.
B. for every real number there is only one corresponding point on the number line
If point P corresponds to a real number x then we say “The coordinate of point P is x” and it is
written as P(x).
On the given number line above, if the distance between two consecutive integers is taken as 1
unit;
The distance between A(1) and B(2), |AB| = 2 – 1 = |1 – 2| = 1 unit
The distance between B(2) and D(–1) |BD| = 2 – (–1) = |–1 – 2| = 3 units
As a result, the distance between A(x 1) and B(x 2) is denoted by |AB| and |AB|=|x 2 −x 1|
Ex: Find the distance between A(3) and B(8)
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102math-wb-w3-(Vector)
