Let A, B, and C denote the vertices of a triangle. Let 0 < r < 1. If P1 is the poi...

Let A, B, and C denote the vertices of a triangle. Let 0 < r < 1. If P₁ is the point on located r times the distance from A to B and P₂ is the point on located r times the distance from A to C, use vectors to show that is parallel to and has r times the length of . (This result generalizes that of Example 6 of this section.)