Final answer:
The correct ordered pair to complete a parallelogram with the given points (2, 1), (6, 1), and (8, 6) is (2, 6), as it maintains parallel and equal length sides.
Step-by-step explanation:
Leanne plotted the points (2, 1), (6, 1), and (8, 6) on a coordinate plane. To complete a parallelogram, the fourth point must be in line with the other points, ensuring the opposite sides are parallel and equal in length. To find the correct ordered pair, examine the patterns of the x and y coordinates. Between points (2, 1) and (6, 1), the x-coordinate increases by 4 while the y-coordinate remains the same, indicating a horizontal line segment. The same horizontal distance must be replicated for the line segment that will connect the points (8, 6) to the fourth point, suggesting the x-coordinate of the fourth point should be 4 less than 8, which would be 4. However, this does not match with any of our answer choices.
Instead, we consider the vertical distance between the points (6, 1) and (8, 6), which is a change of 5 in the y-coordinate with a change of 2 in the x-coordinate. To maintain the properties of a parallelogram, we should have a point that is also 5 units above the point (2, 1), giving us a new point at (2, 6). This matches one of our choices. Therefore, the correct option is d) (2, 6).