If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.

Explanation

To find the value of \( p \) such that the points \( A(6, 1) \), \( B(8, 2) \), \( C(9, 4) \), and \( D(p, 3) \) are the vertices of a parallelogram, we can use the property that the diagonals of a parallelogram bisect each other.

### Step-by-Step Solution:

1. **Identify the Midpoints of the Diagonals**:
The diagonals of the parallelogram are \( AC \) and \( BD \). We will find the midpoints of these diagonals.

- The midpoint \( M_{AC} \) of diagonal \( AC \) can be calculated using the formula:
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