Final answer:
Segments AB and CD are neither parallel nor perpendicular because their slopes are -1/4 and 3/4, respectively. The product of their slopes is not -1, indicating they are not perpendicular,
Step-by-step explanation:
The correct answer is option C. Neither. To determine the relationship between two segments, we need to compare their slopes. For segments AB and CD, we find their slopes using the formula slope = (y2 - y1) / (x2 - x1). For segment AB, using the points (-8, -1) and (-4, -2):
slope of AB = (-2 + 1) / (-4 + 8) = -1 / 4
For segment CD, using the points (0, -3) and (12, 6):
slope of CD = (6 + 3) / (12 - 0) = 9 / 12 = 3 / 4
The slopes of AB and CD are different, meaning they are not parallel. To determine if they are perpendicular, we need to see if the product of their slopes is -1. In this case:
-1/4 * 3/4 = -3/16
Since the product of their slopes is not -1, segments AB and CD are not perpendicular either. Therefore, they are neither parallel nor perpendicular.
To determine if segments AB and CD are parallel, perpendicular, or neither, we can compare the slopes of the two segments. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1).
For segment AB, the two points are (-8, -1) and (-4, -2). Using the slope formula, we get m(AB) = (-2 - (-1)) / (-4 - (-8)) = -1/4.
For segment CD, the two points are (0, -3) and (12, 6). Using the slope formula, we get m(CD) = (6 - (-3)) / (12 - 0) = 9/12 = 3/4.
Since the slopes of AB and CD are not equal and not negative reciprocals of each other, the segments are neither parallel nor perpendicular.