, and are three vertices of a parallelogram .
If is the midpoint of , find the area of .
Step 1: Determine the coordinates of the point
It is given that is a parallelogram and , and .
Let us assume that .
The midpoint of the diagonal is .
As the diagonals of a parallelogram bisect each other, thus is also the midpoint of .
The midpoint of the diagonal can be given by,
So,
So,
Therefore, the coordinate of the point is .
Step 2: Determine the coordinates of the point
The point is the midpoint of and .
Thus, .
Therefore, the coordinate of the point is .
Step 3: Determine the area of
The coordinates of the vertices .
It is known that the area of a triangle with vertices can be given by .
Thus, the area of
Hence, the area of is .