Final answer:
The line segments defined by points A(-2, -11), B(6, 5) and D(-7, -10), F(2, 8) are parallel to each other as determined by their equal slopes.
Step-by-step explanation:
To determine if the line segments defined by pairs of points A(-2, -11), B(6, 5) and D(-7, -10), F(2, 8) are parallel, perpendicular, or neither, we first need to find the slopes of the lines AB and DF. The slope of a line through points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
For AB, the slope mAB is (5 - (-11)) / (6 - (-2)) = 16 / 8 = 2. For DF, the slope mDF is (8 - (-10)) / (2 - (-7)) = 18 / 9 = 2. Since both slopes are equal, the lines AB and DF are parallel to each other.
If the slopes were negative reciprocals of each other, the lines would be perpendicular. For example, if mAB was 2 and mDF was -1/2, they would be perpendicular. However, since both slopes are 2, they are parallel and not perpendicular.