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 solve the problem of finding 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 will follow these steps:

### Step 1: Use the Midpoint Formula
Since the diagonals of a parallelogram bisect each other, we can find the midpoint of the diagonals \( AC \) and \( BD \) and set them equal to each other.

The midpoint \( O \) of \( AC \) is given by:
\[
O = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + a}{2}, \frac{-2 + 2}{2} \right) = \left( \frac{1 + a}{2}, 0 \right)
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