We can compare the slopes of the two segments. Two segments (and two lines in general) are parallel if they have the same slope. The slope is computed as
[tex] m_{AB} = \cfrac{\Delta y}{\Delta x} = \cfrac{B_y-A_y}{B_x-A_x} [/tex]
In this case, we have
[tex] m_{AB} = \cfrac{0-0}{x_2-0} = 0 [/tex]
and
[tex] m_{DE} = \cfrac{\frac{y_1}{2}-\frac{y_1}{2}}{\frac{x_1+x_2}{2} - \frac{x_1}{2}} = 0 [/tex]
Since both segments have the same slope, namely 0, they are parallel.
