To determine whether ABCD is a parallelogram, we need to compare the slopes of its opposite sides.
Let's start by finding the slopes of the two pairs of opposite sides:
1. Slope of AB:
Slope = (y₂ - y₁) / (x₂ - x₁)
= (2 - 0) / (-2 - 2)
= 2 / -4
= -1/2
2. Slope of CD:
Slope = (y₂ - y₁) / (x₂ - x₁)
= (6 - 8) / (6 - 2)
= -2 / 4
= -1/2
Now let's compare the slopes of both pairs of opposite sides. If the slopes are equal, then the opposite sides are parallel.
The slopes of AB and CD are both -1/2. Since the slopes are equal, we can conclude that the opposite sides AB and CD are parallel.
Therefore, ABCD is a parallelogram because its opposite sides AB and CD are parallel.