If A(-2, -1), B(a,0), C(4,b) and D(1,2) are the vertices of a parallelogram. Complete activity to find the values of a and b.
Activity :
A(-2,-1), B(a,0), C(4,b) and D(1,2) are the vertices of a parallelogram
Diagonals of parallelogram bisect each other
`:.` midpoint of diagonal AC = Midpoint of diagonal BD
By midpoint formula,
`((-2 + 4)/(2), (-1 + b)/(2)) = ((a + 1)/(2), (square)/(square))`
`:. (square, (-1 + b)/(2)) = ((a + 1)/(2), 1)`
`{:( :. square = (a + 1)/(2)),("on simplifying, we get"),(a = square):}|:{:((-1 + b)/(2) = square),("on simplifying, we get"),(b = square):}`

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 will use the property that the diagonals of a parallelogram bisect each other. This means that the midpoint of diagonal \( AC \) is equal to the midpoint of diagonal \( BD \).

### Step 1: Find the midpoint of diagonal AC
The coordinates of points \( A \) and \( C \) are:
- \( A(-2, -1) \)
- \( C(4, b) \)

Using the midpoint formula:
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