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Lesson 1.2 Segments and Rays

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To know the definition of a segment

To identify the distance between the points of asegment.

To determine the real number between the two pointsof a segment

To know the definition of a ray

To know the difference of a segment and a ray

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To every pair of distinct points P and Q, therecorresponds a unique positive number called thedistance between P and Q.

P Q

PQ is used to denote the distance betweenthe two points P and Q. The distance

between any point and itself is equal to 0.The distance between two points does notdepend on the order in which the pointsare mentioned. Thus, it is always true thatPQ=QP

d=PQ

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The points of a line can be placed in correspondencewith the real number in such a way that

a. To every point of the line, there corresponds exactly

one real number;b. To every real number, there corresponds exactly one

point of the line; and

c. The distance between any two points is the absolute

value of the difference of their correspondingnumbers.

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The correspondence between the set of real numbers andthe points on a given line is known as a coordinate system.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Coordinate System

The numbercorresponding to a

given point is calledits coordinate.

If the distance between points X and Y withcoordinates x and y is to be computed, then

XY=x - y

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

B I R D S F L Y

a. Distance between D and Y

DY = -1 5 = -6= 6

b. Distance between I and FThe points are evenly spaced;hence, the coordinates of the

other points can be determined.IF=-3 - 3= 6

c. Distance between B and LBL=-4 - 4= 8

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The concept of distance between two points is nowused in order to define betweenness of points

Definition 1.4Point B is said to be between points A and C if and only if

a. A, B, and C are points on the same line, and

b. AB+ BC = AC

Q U I C K S A N D

The symbol A-B-C or C-B-A is used to indicate that point Bis between points A and C. Which of the points shownbelow are between points Q and D? C and N? U and S?

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For any two points A and B, the segment AB is theunion of A and B, and all points that are betweenthem. The points A and B are called the endpoints of

AB

A B

A beam of light coming from a source representsanother geometric figure called a ray. The source oflight becomes its endpoint, and all the points on thepath of the beam that extends without end are included

in the ray.

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