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Postulate: The Ruler Postulate
The points on any line can be paired with the real numbers in
such a way that:
- Any two chosen points can be paired with 0 and 1.
- The distance between any two points in a number line is
the absolute. value of the difference of the real numbers
corresponding to the points.
By virtue of the Ruler Postulate, a system to determine the
length of a segment, which is equal to the distance between its
endpoints, can be formulated. Every point on a number line can be paired
to a real number; it is called the coordinate of the point. The
length of a segment is found by determining the difference between
the coordinates of its endpoints and taking the absolute value.
Ex.
The coordinate of
A = -4.
B = -2
O = 0
C = 3
P = 5
The length of segment BC is determined as follows:
B has coordinate -2 , C has coordinate 3
-2 - ( 3 ) = -5
| -5 | = 5 \ the length of segment BC is 5.
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