Final answer:
The coordinates of point D in the parallelogram ABCD were calculated using the properties of a parallelogram and the given vertices. However, the calculated result does not match any of the provided options, suggesting an error in the calculation or question.
Step-by-step explanation:
The question involves finding the coordinates of point D to complete the parallelogram ABCD with given vertices A(5,4), B(-1,-2), and C(8,-2). To do this, we can use the properties of a parallelogram, which state that opposite sides are equal in length and parallel. Since AB and CD are opposite sides of the parallelogram, they must be equal and parallel. Therefore, the vector from A to B should be the same as the vector from D to C. To find the vector AB, we subtract the coordinates of B from A: (5 - (-1), 4 - (-2)) = (6, 6). Then we subtract this vector from C to find the coordinates of D: (8 - 6, -2 - 6) = (2, -8). However, none of the given options match this result. There might be a mistake with either the calculation or the provided options.