Final answer:
The lines DE and GH are neither parallel nor perpendicular to each other.
Step-by-step explanation:
The given points are D(-2, 1), E(6, 3), and H(3, -2).
To determine if lines DE and GH are parallel, perpendicular, or neither, we can calculate the slopes of both lines.
The slope of line DE can be calculated using the formula:
m = (y2 - y1) / (x2 - x1).
Substituting the coordinates of D and E, we get :
m(DE) = (3 - 1) / (6 - (-2))
= 2 / 8
= 1/4.
Similarly, the slope of line GH can be calculated using the formula:
m(GH) = (-2 - 3) / (3 - (-2))
= -5 / 5
= -1.
Since the slopes of line DE and GH are not equal or negative reciprocals of each other, the lines are neither parallel nor perpendicular to each other.