Final answer:
Lines AB and CD have the same slope of -1/3, which means they are parallel. They are not perpendicular since their slopes are not negative reciprocals of one another.
Step-by-step explanation:
To determine whether the lines are parallel, perpendicular, or neither, we need to find the slopes of the lines formed by the points A(1,5), B(4,4), and C(9,-10), D(-6,-5).
First, we find the slope of the line AB. The slope formula is (y2 - y1) / (x2 - x1). Applying this to points A and B:
Slope of AB = (4 - 5) / (4 - 1) = -1 / 3
Next, find the slope of line CD:
Slope of CD = (-10 + 5) / (9 + 6) = -5 / 15 = -1 / 3
Since the slopes of both lines AB and CD are equal, lines AB and CD are parallel.
To check if lines are perpendicular, we would look for the slopes to be negative reciprocals of each other. In this case, they are not, so the lines are not perpendicular.