If the points A (1,-2), B (2,3) , C (a,2) and D (-4-,3) form a parallelogram , them find the value of a and height of the parallelogram taking AB as base.

Explanation

To find the value of \( a \) and the height of the parallelogram formed by the points \( A(1, -2) \), \( B(2, 3) \), \( C(a, 2) \), and \( D(-4, 3) \), we can follow these steps:

### Step 1: Use the property of the midpoint of diagonals
In a parallelogram, the diagonals bisect each other. Therefore, the midpoint of \( AC \) should be equal to the midpoint of \( BD \).

**Midpoint of \( AC \)**:
\[
\text{Midpoint of } AC = \left( \frac{1 + a}{2}, \frac{-2 + 2}{2} \right) = \left( \frac{1 + a}{2}, 0 \right)
...