Question

Are lines DE and GH parallel, perpendicular, or neither for D(-2, 1),

E(6, 3), G(-1, 14), and H(3,-2)? Justify your reasoning.
A. Parallel; the two lines have the same slope.
B. Perpendicular; the product of the slopes of the lines is -1.
C. Neither; the lines do not have the same slope and the product of the slopes is not -1.
D. Neither; the slope of GH is the negative reciprocal of the slope of DE

Answer 1

Lines DE and GH are neither parallel nor perpendicular because their slopes are not equal and the product of their slopes is not -1.

Step-by-step explanation:

The slope of a line can be calculated using the formula: slope = (change in y) / (change in x). To determine if lines DE and GH are parallel or perpendicular, we need to find their slopes. Line DE has points D(-2, 1) and E(6, 3), so its slope is: (3 - 1) / (6 - (-2)) = 2 / 8 = 1/4. Line GH has points G(-1, 14) and H(3, -2), so its slope is: (-2 - 14) / (3 - (-1)) = -16 / 4 = -4.

Since the slopes of DE and GH are not equal, they are not parallel. Additionally, the product of their slopes is not equal to -1, so they are not perpendicular either. Therefore, the correct answer is: D. Neither; the slope of GH is the negative reciprocal of the slope of DE.