Answer:
Sure, I'd be happy to help! To determine if the two line segments AB and CD are parallel, perpendicular, or neither, we can use the slope formula.
The slope formula is:
Slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Let's apply this formula to the two line segments:
AB:
(x1, y1) = (3, 7)
(x2, y2) = (-6, 1)
Slope = (y2 - y1) / (x2 - x1) = (1 - 7) / (-6 - 3) = -6/3 = -2
CD:
(x1, y1) = (-6, -5)
(x2, y2) = (0, -1)
Slope = (y2 - y1) / (x2 - x1) = (-5 - (-1)) / (-6 - (-6)) = -4/5 = -0.8
Now, let's compare the slopes of the two line segments:
AB: Slope = -2
CD: Slope = -0.8
Since the slopes are different, we can conclude that the line segments AB and CD are not parallel. In fact, we can see that AB is steeper than CD, because the slope of AB is more negative.
Therefore, the correct answer is:
The two line segments AB and CD are not parallel.
Explanation: