Final answer:
Line d and line e are neither parallel nor perpendicular to each other.
Step-by-step explanation:
Line d passes through points (9, 1) and (2, 5). The slope of line d can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of line d:
slope = (5 - 1) / (2 - 9)
slope = 4 / -7
Therefore, the slope of line d is -4/7.
Line e passes through points (9, 7) and (7, 4). The slope of line e can be calculated using the same formula:
slope = (4 - 7) / (7 - 9)
slope = -3 / -2
Therefore, the slope of line e is 3/2.
Since the slopes of line d and line e are -4/7 and 3/2 respectively, and the product of their slopes is not -1, line d and line e are not perpendicular. However, as the slopes are not the same, line d and line e are not parallel either. Therefore, line d and line e are neither parallel nor perpendicular to each other.