Final Answer:
C. (2,-8), The combination of a positive y-direction translation, positive x-direction translation, and x-axis reflection places vertex Q at (2,-8).
Step-by-step explanation:
After performing the given transformations on the parallelogram, the vertex Q ends up at the coordinates (2,-8). First, a translation of 2 units in the positive y-direction moves Q to (2,0).
Then, a translation of 6 units in the positive x-direction places Q at (8,0). Finally, reflecting about the x-axis negates the y-coordinate, resulting in the final position of Q at (8,0) after reflection, which simplifies to (2,-8).
The initial translation in the positive y-direction shifts the point vertically, bringing Q to (2,0). Subsequently, the translation in the positive x-direction moves the point horizontally, placing it at (8,0).
The reflection about the x-axis negates the y-coordinate, resulting in the final position of Q as (2,-8). Each transformation contributes to the overall change in position, and the order of transformations is crucial in determining the final coordinates.
Therefore the correct option is C. (2,-8).