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Directed Line Segment

Figure 10.1.1 shows a directed line segment from the point P to the point Q.


Figure 10.1.1

We pictorially represent a directed line segment as an arrow from P to Q, and use the symbol 10_vectors-2.gif. Mathematically, a directed line segment is most easily represented as an ordered pair of points.

The directed line segment from P to Q, in symbols 10_vectors-3.gif, is the ordered pair of points (P, Q). P is called the initial point, and Q, the terminal point, of the directed line segment.

The directed line segments 10_vectors-4.gif and 10_vectors-5.gif are considered to be different, 10_vectors-6.gif has initial point Q and terminal point P. If P(pl, p2) and Q(qt, q2) are two points in the plane, the x-component of 10_vectors-7.gif is the increment ql - p1 of x from P to Q, and the y-component is the increment q2 - p2 of y, as shown in Figure 10.1.2.

x-component of 10_vectors-8.gif= qx - px. y-component of 10_vectors-9.gif= q2 - p2.


Figure 10.1.2

Last Update: 2006-11-25