Question

Line v passes through points (8, 2) and (1, 10). line w passes through points (5, 11) and (10, 7). are line v and line w parallel or perpendicular?

Answer 1

Line v and line w are neither parallel nor perpendicular because their slopes, -8/7 and -4/5 respectively, are neither equal nor is their product equal to -1.

Step-by-step explanation:

To determine if line v and line w are parallel or perpendicular, we first need to calculate the slopes of each line. The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

For line v passing through points (8, 2) and (1, 10), the slope is:

mv = (10 - 2) / (1 - 8) = 8 / -7 = -8/7

For line w passing through points (5, 11) and (10, 7), the slope is:

mw = (7 - 11) / (10 - 5) = -4 / 5 = -4/5

Lines are parallel if they have the same slope and perpendicular if the product of their slopes is -1. In this case, the slopes are -8/7 and -4/5, which are neither equal nor do they multiply to -1.

Thus, line v and line w are neither parallel nor perpendicular.