Use the slopes of AB and CD to determine whether AB and CD are parallel, perpendicular, or neither.
A(-8,5) B(-2,-4) C(6,0) D(0,-4)
AB has slope (-4-5)(-2-(-8)) = -9/6 = -3/2
CD has slope (-4-0)/(0-6) = -4/-6 = 2/3
so, they are ???
To determine whether AB and CD are parallel, perpendicular, or neither, you need to calculate the slopes of the two lines, AB and CD, and compare them.
The formula to calculate the slope of a line passing through two points, (x₁, y₁) and (x₂, y₂), is given by:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slopes of AB and CD:
AB slope = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 5) / (-2 - (-8))
= (-9) / (6)
= -3/2
CD slope = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 0) / (0 - 6)
= (-4) / (-6)
= 2/3
Now, compare the slopes:
If the slopes of AB and CD are equal, then the lines are parallel.
If the slopes of AB and CD are negative reciprocals of each other (opposite signs and reciprocal values), then the lines are perpendicular.
If the slopes of AB and CD are neither equal nor negative reciprocals, then the lines are neither parallel nor perpendicular.
Comparing the slopes of AB and CD, we can see that the slopes are neither equal nor negative reciprocals:
AB slope = -3/2
CD slope = 2/3
Therefore, AB and CD are neither parallel nor perpendicular.