Show that the line joining one vertex of a parallelogram to the mid-point of an opposite side trisects the diagonal and is trisected there at.

Explanation

To show that the line joining one vertex of a parallelogram to the midpoint of an opposite side trisects the diagonal and is trisected there, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Parallelogram**:
Let the vertices of the parallelogram be denoted as \( O, A, B, C \) where \( O \) is the origin, \( A \) is at position vector \( \mathbf{a} \), \( B \) is at position vector \( \mathbf{b} \), and \( C \) can be expressed as \( \mathbf{a} + \mathbf{b} \).

2. **Identify the Midpoint**:
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