Final answer:
Quadrilateral ABCD with the given vertices is a parallelogram. If the vertex C is shifted to C'(11, 1), the resulting quadrilateral ABC'D would remain a parallelogram. This concept relates to graphical methods for finding vector resultants.
Step-by-step explanation:
To solve the given problem, we need to analyze the properties of quadrilateral ABCD with vertices A(11, -7), B(9, -4), C(11, -1), and D(13,-4). By looking at the coordinates, we can see that AB and CD are parallel since the x-coordinates for A and B differ by 2, which is the same difference as between C and D. This suggests that ABCD could be a trapezoid or a parallelogram. However, notice that AD and BC are also parallel because both vertical segments have an x-coordinate difference of 0, indicating that quadrilateral ABCD is in fact a parallelogram.
Next, if the vertex C(11, -1) were shifted to C'(11, 1), then CC' would represent a vertical translation upward by 2 units. With C moving to C', the shape of the quadrilateral would still be a parallelogram because the sides will remain parallel and equal in length. Vertices A, B, and D remain fixed while only C is translated, thus maintaining the parallel nature of opposite sides.
We can further categorize this particular parallelogram based on additional properties, such as side lengths and angles, if more information is provided. Without it, we can refer to the example of finding vector resultants from the given questions. For instance, when finding the resultant of vectors A and B graphically, we would construct a parallelogram and use the diagonal as the resultant, similar to the concept of parallelogram sides in ABCD being equal. The same parallelogram approach is used to find other vector resultants or differences, such as C + B, D + E, or A - 4D + 2E.