Final answer:
By calculating the slopes of the lines AB and CD, we find that they are negative reciprocals of each other, indicating that lines AB and CD are perpendicular.
Step-by-step explanation:
To determine if the lines AB and CD are parallel, perpendicular, or neither, we must calculate the slopes of the lines that pass through the given points.
For line AB, the slope (m) can be calculated using the coordinates of points A(1, 9) and B(7, 4).
mAB = (y2 - y1) / (x2 - x1)
mAB = (4 - 9) / (7 - 1)
mAB = -5 / 6
Similarly, for line CD using the coordinates of points C(8, 13) and D(-2, 1):
mCD = (y2 - y1) / (x2 - x1)
mCD = (1 - 13) / (-2 - 8)
mCD = -12 / -10
mCD = 6 / 5
Since the slopes are negative reciprocals of one another (mAB = -5/6 and mCD = 6/5), this indicates that lines AB and CD are perpendicular to each other, forming a 90° angle.