Of `A(-2,-1),``B(a ,0),``C(4, b)` and `D(1,2)` are the vertices of a parallelogram, find the values of `a` and `b`.

Explanation

To find the values of \( a \) and \( b \) for the vertices \( A(-2, -1) \), \( B(a, 0) \), \( C(4, b) \), and \( D(1, 2) \) of a parallelogram, we can use the property that the diagonals of a parallelogram bisect each other. This means that the midpoint of diagonal \( AC \) should be equal to the midpoint of diagonal \( BD \).

### Step-by-Step Solution:

1. **Find the Midpoint of Diagonal AC:**
The coordinates of points \( A \) and \( C \) are \( A(-2, -1) \) and \( C(4, b) \).
The midpoint \( O \) of \( AC \) can be calculated using the midpoint formula:
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