Final answer:
To find the coordinates of vertex Z of the parallelogram, we can use the fact that opposite sides of a parallelogram are equal in length. The coordinates of vertex Z are (-5, -9). The area of the parallelogram can be found using the formula base x height, which gives us an area of sqrt(697).
Step-by-step explanation:
To find the coordinates of vertex Z, we can use the fact that opposite sides of a parallelogram are equal in length. Since we know the coordinates of vertices W, X, and Y, we can find the coordinates of Z by finding the coordinates of the fourth vertex using the formula:
Z = X + Y - W
Substituting the given values, we have:
Z = (-4,-4) + (-1,-4) - (0,1)
Simplifying, we get:
Z = (-4 + -1 - 0, -4 + -4 - 1) = (-5, -9)
To find the area of the parallelogram, we can use the formula:
Area = base x height
The base can be found by finding the distance between two adjacent vertices, and the height can be found by finding the distance between one side and the opposite vertex. Using the distance formula, we find that the base is sqrt((-4-0)^2 + (-4-1)^2) = sqrt(41), and the height is the distance between vertex Z and side XY, which is sqrt((-4--5)^2 + (-4--9)^2) = sqrt(17). Therefore, the area of the parallelogram is sqrt(41) x sqrt(17) = sqrt(697).