Example 6: Finding the Midpoint of a Line Segment

Find the midpoint of the line segment from A(- 1, 2) to 5(3, 3) (Figure 10.2.12).

Figure 10.2.12

The points have position vectors

A = -i + 2j. B = 3i + 3j.

The midpoint P has the position vector

P = ½A + ½B = ½(-i + 2j) + ½(3i + 3j) = i + (5/2)j.

Therefore P is the point (1, 5/2).