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 . 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 , 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 and are considered to be different, has initial point Q and terminal point P. If P(p_l, p₂) and Q(q_t, q₂) are two points in the plane, the x-component of is the increment q_l - 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 = q_x - p_x. y-component of = q₂ - p₂.

Figure 10.1.2