Answer:
To determine whether AB and CD are parallel, perpendicular, or neither, we need to analyze their slopes.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slopes of AB and CD:
AB:
Point A (8, 4)
Point B (4, 3)
slope of AB = (3 - 4) / (4 - 8) = -1 / -4 = 1/4
CD:
Point C (4, -9)
Point D (2, -1)
slope of CD = (-1 - (-9)) / (2 - 4) = 8 / -2 = -4
Now, let's analyze the slopes:
1. If the slopes of AB and CD are equal, then the lines are parallel.
In this case, the slope of AB is 1/4 and the slope of CD is -4. Since the slopes are different, AB and CD are not parallel.
2. If the product of the slopes is -1, then the lines are perpendicular.
In this case, the product of the slopes of AB and CD is (1/4) * (-4) = -1. Since the product is -1, AB and CD are perpendicular.
Therefore, AB and CD are perpendicular to each other.
In summary, AB and CD are perpendicular lines.
Explanation:
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